I usually tend to recommend Onkyo and Denon, since their more recent models include Audyssey room correction. While Audyssey will not solve all acoustic problems, it can improve things immensely... especially when the speakers hooked up have serious shortcomings.
I don't really know any details about the speakers you bought. It appears that Acoustic Research was a solid company "back in the day", but they were sold to Audiovox recently. (Appears to be the same story with Advent and RCA?)
I'm not big on the history of speaker companies since I'm only 26 years old, but it appears that Audiovox is generally putting out a lot of really cheap stuff.
I tried searching on AVSforum for more info on them, but I didn't really come up with anything (which is usually a bad sign).
I suspect that the set you have from Best Buy would benefit greatly from a receiver that can do some automatic equalization on it.
The following clip is kind of dependent on having something decent to listen through, but here is a test I did with a set of $60 sony speakers and Audyssey MultEQ-XT.
http://www.youtube.com/watch?v=jmmDenKL4U0
(The "more info" description describes the test and my take on the results)
If you get a really basic receiver off craigslist or something, you'll be able to get everything going, but you're not going to get the most out of the speakers you bought. It will still be a big step over TV speakers of course, so maybe that's good enough for you. This comes down to how much you care about this stuff.
If music is not a priority, then shortcomings in the set are probably going to be harder to notice.
If your TV has enough HDMI inputs for your sources, then having HDMI on the receiver is not really necessary.
If you get a receiver without HDMI capability (or a receiver WITH HDMI but not AUDIO over HDMI), then you'll be running a separate cable for each source for the audio.
A receiver with HDMI would make it easier to switch between sources with one remote... and could potentially reduce cable clutter depending on the capabilities of the receiver.
Without knowing how picky you are about this stuff, it's difficult to make a recommendation on this. It's possible that you could buy a $100 receiver and be extremely happy with things. It's also possible that you could get a $400 receiver that does good auto calibration, and has all the HDMI goodies... but you might still be unsatisfied and desire a speaker upgrade right away.
If you have any places around you that would allow for you to demo some different products, that would give you an idea of the difference between a $150 5.1 setup and a $1500 5.1 setup.
Some places will have dedicated spaces to make those comparisons relatively quickly and easily. (as compared to a row of sets on a shelf where there are a ton of variables to consider in addition to just what product is turned on).
If this is something you're thinking about upgrading later, it might make sense to just get a solid receiver now, so that when it comes time to upgrade... you're not considering upgrading the receiver again too.
If you're the kind of person who tweaks and upgrades things a lot, it might be cheaper to just "do it right" the first time with the receiver.
Before these automatic room correction solutions, I would have told you that it was a total waste to pair up a $150 5.1 set of speakers to a $300-$400 receiver. It's still not optimal for spending, but a good receiver can make a cheap set of speakers sound a whole heck of a lot better.
There was a deal yesterday on a Denon 1910 for $362 which was a good deal, but that's dead now. The Onkyo 160 or 607 would be solid choices as well.
These are all above your stated pricerange though, so I don't know how flexible you are on this... or really how much you care about all this.
As for hooking things up, we can help you with that. Once you learn what all the parts on the back of the receiver do, it's a lot easier to swallow.
Once you buy something, I can help you with diagrams and such. There are also some settings you'll want to adjust within the receiver's menu to get the most out of things (regardless of whether you spend $100 or $400 on a receiver).