LostInSpace927, cat6 vs. cat5e is a mostly different problem than 100 vs. 1000(gigabit), and only the latter should be able to affect your latency unless something's already very broken (if you currently have bad cable, fixing that is good). Gigabit might reduce your latency because the delay to move the data across the link is lower, but it might also INCREASE your latency because the 1000BaseT physical layer has inherently higher latency requirements in its designs (a whole lot of DSP voodoo going on down there). Gigabit might also be good because most gigabit NICs are just plain better designs than many 10/100 NICs, especially when compared to the cheap 10/100 NICs.
cat5e vs. cat6 is precisely an issue of the signalling specs of the cable plant, that is, bandwidth and some other electrical performance parameters. For 10, 100, or 1000, either cable will technically work. Cat6 cable will be higher-quality in general, and will have a lot more electrical performance headroom versus cat5e, so in cases where signal quality could be marginal causing frame loss on a cat5e cable system, you might not have that problem with cat6. That's the main reason to get cat6, really - better electrical performance all around, more headroom to compensate for other problems you might have.
Bottom line, though: The same two 10/100 devices over a cat5e cable and a cat6 cable, if there are no signal quality problems, will perform exactly the same. The thing cat6 buys you in this case is that there might not be signal quality problems in cases where there would be with cat5e.
EIA 568A & 568B basically have to do with what colors on the cable map to which pins on the RJ45 plug/jack. Either standard will work fine for Ethernet, either way the things that need to be paired together end up on paired together. 568B is the American standard, and 568A is for most of the rest of the world. If you wire with 568A, we'll tell all your FPS buddies that you wired up your house like a Frenchman, and I'm sure they'll express their opinion on that in an appropriate manner
Running cable outside is a very bad idea unless you know what you're doing. At the very least, please enclose it in an insulated (read: plastic) conduit tubing. I strongly urge you to go down to your local Home Depot and find the guy in the electrical aisle who was an electrician for thirty years, those are the kind of guys who can tell you exactly what to get and how to do it. Just use the magic words "low voltage wiring" to explain what you're doing, or "telephone wiring" if they still get confused. "Current carrying" wiring is the primary domain of electricians and carries a MUCH stricter set of rules. Lightning is a potential problem because lightning strikes the ground and the earth potential nearby the strike can change dramatically, but if it's truly under your house it would stand to reason that lightning would hit your house, in which case you have a different problem, or hit beside your house, in which case it should be far enough away to not be as bad a problem. Water / moisture is also a problem to watch carefully for, water does all sorts of very ugly things to the performance of cable and normal indoor cable does not protect against that.
Aside: anyone know of cat5e / cat6 designed for buried service wire use, jacketed with something strong and filled with that horrible icky goo that telco BSW uses?