Don't know how I missed this thread before, great idea you have and by the sounds of it you can't fail. Great plan with good location and lots of drive, best of luck

Now onto that feedback-
1. Business Setup. --
Sounds like you already have much of it figured out, if I was you I would suggest pushing the membership route as much as possible. Relying on hourly business tends to be a lot more nerve racking, and also can make it more difficult to build a customer base in such an environment. Someone sittng around bored at home may decide to drop by and spend some cash, someone with a membership would be far more likely to do the same though, and having an environment where you are pretty much assured of finding some "live" competition should help in promoting your business. I would strongly reccomend having a snack bar of sorts, include things like pizza and chips(with a no eating at the PC rule if it makes you nervous) as both a convenience factor for your customers and an added source of revenue.
Selling merchandise and handling upgrades on site sound like excellent ideas. Another may be assmebling entire systems for people to nervous to do so. I don't know how much of a market there would be for such a thing, but it is mearly an extension of handling upgrades and would allow users with enough sense to chose all the right parts, but without the confidence to build it themselves, to have a fully customized PC. Another possible option is to offer clones of what you are running for your systems. For users with older computers that frequent your business, they may feel comfortable knowing
exactly how their system will run using their favorite games. Offering them a replica of exactly what you use would be a way to ensure them satisfaction at least in terms of their gaming which tends to be high priority for the type of customer you are looking for. This would require only the amount to build the first system for startup and then would be relatively self maintaining as far as revenue, assuming that you are dealing with savvy customers that keep support issues to a minimum. Most of this probably falls more under operations setup, so I'll go to point 2.
2. Actuall Site setup. --
The physical layout I assume? I would attempt to go with a "business" type setting, avoiding the cubicle feel as much as possible. If you are using dividers that look like cubicles, paint them black and slap on some quick gamers logos(nV's eye, 3dfx, id etc) or something, anything to make it feel more relaxed. May sound like a simple thing, try having a few different types of chairs available. If everyone who goes there, or almost everyone, finds a very comfortable spot to sit, it helps the overall customer experience. A minor thing that may easily be overlooked but truly makes a difference in the overall experience. I'm willing to pay a 50% premium($3-$4) for tickets to a movie that has very comfortable seats over the extremely cramped and backache inducing ones most theaters have.
Having seperated cluster for different types of gaming. You could utilize your business to do such things as host the local chess tournament, just as an example, and that probably wouldn't mesh well with the frag fest going on with another group. Keeping cluster of PCs could help you to keep oponents close to each other so trash talking may occur easily, while eliminating as many exterior factors as possible. A setup as portable as possible, in terms of being able to adjust the setup, would probably be best. That way, you can alter the floor to best accomodate differing needs. If Half-Life is extremely popular, you could add onto the Half-Life cluster while pulling units from the Quake3 cluster(just an example).
Another thing I would suggest is a TV with cable or DVD/VCR combo. This isn't to encourage a hangout mentality, but to give people something to do while eating some pizza or in case of customer overflow. Give them something to keep them there until it is their turn to play, and in turn keeps them coming back.
3. Operations of center. --
I would say most importantly not to limit yourself based on the games that we like the most. By this I mean keep your options open to the broader scope of the populace, but without dilluting your core group. For instance, the chess tournaments I mentioned above while clearly not the traditional PC gaming, may generate some interest amongst casual hobbiests. Another example could be racing tournaments or something like having a monthly track selected and whoever finishes with the best time wins a prize. Easy to keep going with all the possibilities, and I know that it has already been mentioned and you already stated support but it can be such a huge selling point that it should be mentioned again. Of course, you might even be able to get away with a FPS tournament and find some interest
4. Web presence and role of web. --
I can see you using the web as an added bonus aspect for your business in a couple of different ways. One clearly is offering a fast internet connection, the question is how fast will it be and will you allow people to DL content to removeable media to take with them? I don't know about other people, but I know I would pay for a membership simply for that reason, the rest would be some truly nice gravy. Being stuck on dial up and needing to DL multiple 30-50MB patches on top of trying to check out demos and regular software patches etc is a pain. Offering a service to burn patches etc onto a CD-R, for an added fee of course and for members only

, could be a nice added service though it may in fact be a much larger pain to keep up then it is worth. That is one oddball one that may not have been though of, or may have been and was thrown out for the administrative pain it would be.
One area, for promoting your place and adding a sense of "community" could be an up to date score tracker of sorts, logging all information for games played on site and keep track of ongoing tournaments and weekly or monthly challenges if you have them- perhaps an auto updating site via the server(I don't know how that would work, that isn't my area). Also a member BBS to promote the ever important discussion/trash talking and help to give an entire sense of community. I know that I would take a four hour drive and pay money to get a chance to meet many members of this BBS and enjoy some time gaming with them side by side, let alone a quick trip to a place I have a membership for.
Another possibility that could eliminate geography in terms of promotions, have a "design the best Q3/UT etc level contest and use that for a championship tournament round(keep the finalists blind to the map until showtime and then offer it to members). This is a contest you could also start on a local basis and on the web before everything is setup. Have a large tournament opening weekend using that map or all of the maps that are decent to keep everyone off balance. The contest itself, particularly if giving away a half way decent prize, will generate word of mouth on its own and bring an extra challenge to the table for a competitive environment.
5. Sell product? --
Absolutely. What to sell, and how much to stock is the tricky part but I'm sure you have a better grasp as to the amount of possible traffic and also the economic conditions in your area.
6. Business partnerships. --
This could be tricky in some aspects. If you drop selling of computer related material, you could probably bag any local shops easily. Even if you do sell products that may still work for you, you could use them as a distributor of sorts if a deal could be struck. Split the profits with them, and let them handle inventory. You could use it as a small revenue generator and a larger promotional tool, and leave the handling of goods to them for the most part. This simplifies your end of dealing with things, though striking an acceptable deal could be a bit more difficult. Intel would be real nice to bag, offer some Intel Inside logo promise, a large logo of some sort, for possible reduced prices or promotional aids? I don't know what type of work would be involved in landing such a deal, what type of control do the local operations have over such things as promotions?
7. Alliances to join. --
Any gamers league you can find and if you can't find one, make one yourself to start with. Great promotional tool and also a bit of free(or reduced) advertisement when they have events. Other then that I must say I have no idea without knowing the makeup of your local businesses. In the broader sense it ties in with issue 9.
8. Advertising. --
Word of mouth is the best type, no doubt. For initial advertsising I would suggest local HS, any and all PC shops you can find, grocery stores, retail stores and of course word of mouth. Start talking now, and trying to spread as much hype as you can to get people talking. Something along the lines of "10-10-2000- Untamo Gaming Center- Think you have game?
www.untamo.com" Or some other such thing that is cheesy enough to stick in people's heads. Combined with word of mouth it should help to generate some hype. With the limits of 24-32 machines I wouldn't go overboard with advertising budgets, use word of mouth as much as possible and set up a web site ASAP promoting exactly what you will have to offer.
9. Computers. Hardware & Software-
This part is one of the trickiest. Do you play the complete clone game and have all identical machines at the possible cost of alienating partisans? An all Intel situation seems like it could have added benefits beyond any potential hard feelings by the AMD crowd, but 3dfx vs nVidia can cause problems in certain aspects. You want your systems to run games as well as possible, but each offering has strengths and weaknesses and does carry some zealotry weight along with it. Chosing to go entirely one platform can offer you benefits though, you can utilize it for possible perks from say 3dfx or Hercules. Both are very concerned with the image of their companies and being an exclusive provider to a place such as you are working on could be worth far more to them then any possible deals they may be willing to cut on hardware. I think a price per system and when you will be building them would help for the general gaming rig quite a bit.
Servers aren't my thing, I trust that many others on this board have advice far better then what I can give so I'll skip that. Software for OS it seems a no brainer, WindowsME or 98SE depending on when you are building the machines. What games to buy, and how many licenses can be very tricky. UT, Q3 and Half-Life are no brainers, but beyond that it gets more difficult. I would strongly reccomend having a racing game or two or three on hand, but which ones and then you deal with the added expense of steering wheel/pedal controllers(would pretty much be required I would think). For that matter, I would reccomend going with a couple of different makes of joysticks and gamepads to offer to customers, along with a couple of different keyboards and mouse options. The total experience is a big impact IMHO and one of the reasons I spend $8-$12 going to a movie theater even though I have several thousand tied up in my entertainment center.
10 is again best discussed with many others of this board. I'm sorry if I was too long winded or avoided the KISS basis too much, just so many possibilites with this, with your determination I can't see you failing and I know I would love to have a place like this in my area(roughly 3,000 miles away from you). Best of luck to you.