First thing you should do is come on up to NHMS next weekend, and experience it first hand.
Second thing you should do is get your safety gear together and buy an arrive and drive spot on a team. (We occasionally have openings...). Actually being part of the event and driving in it will give you a completely different perspective on the event, and what would be the best way for you to be a part of it.
What are your goals, as you know them now? To run around the track more than anyone else? To bring something obscure/awful/ridiculous and shoot for the top prize (IOE)? To just go out and have some good fun with your buddies and who cares where you finish?? All of these are totally legitimate and good goals, but they certainly play into your car choice. If you want to go fast, you'll need a BMW, Integra, RX7, or something like that. Boring. If you want to go for the gold, you're looking for eastern block stuff, terrible 70's stuff, old detroit iron, french cars, etc, these are awesome. If you just want to run with your buddies, pick the most mundane and reliable car you can reasonably find.
I've done 10 of these so far, been part of the builds for 3 (going on 4), and have raced 8 different cars in Lemons races. All have been class B or C cars. Here's a rundown on my satisfaction with a few of them
-Wartburg: Don't do anything like this for your first build.
-Civic Wagovan 4WD: We had it for free, it is the slightly less boring obscure 4WD version. It is a joy to drive, but oh so slow due to the 4WD. Reliable, as long as you follow a few tricks both in prep and driving.
-Boat: Ridiculous fun, even though it drives like a truck with a boat on it.
-Rolls Royce: I now never want to own a Rolls Royce, but it sure does look good in my driveway.
-Other obscure old british cars (Mini, Moke, Simca 1204, Austin America): fun in their own way, especially the Mini and Moke, but you need to be tapped into the knowledge and parts base to run one well.
We've been lucky with reliability, partially because we hold ourselves to low rev limits (6500 on the Honda, 4400 on the boat's GM 4.3), keeping a little too much of a good oil in the motor, and exercising some mechanical sympathy. We would much rather wrench in the garage at home, so we drive a little tiny bit slower at the track. Someday we will blow something up, but we've been lucky so far.
Overall I'm really happy with what we have, as obviously our goals tend toward the IOE end of the spectrum, and we are doing OK there, and have been doing pretty well in class C lately. We keep trying to make the cars better, and will for a while. It is nice to have the easy car in the Civic that anyone can drive and that has a passenger seat we use for instruction, but it won't ever win anything, which is why we have the other silly cars, really just because we are amused by them, and like to amuse others with them.
As you've read, Lemons reliability isn't like normal car reliability. SBC's blow up because they get revved over 4500, or hopped up, or both. Hondas blow up because they get revved to 7000+ and a lemons grade Honda is usually half blown up when you start, same with Toyotas. Alfas do amazingly well, and RX7s seem to keep running and running. Volvo 240s and Crown Vics also seem to be some of the most reliable cars out there.
So in summary: go to a race to get more data, decide your goals, then pick a car. I happen to know where a mechanically excellent but cosmetically challenged 85 Mercedes 300D turbo is in the Boston area, that could be sold for $500.