how do I decide whether I want 5.1 or 7.1?
IMO, 7.1 isn't really needed, especially when you are just starting out. Not many movies make use of 7 channels, so as you are just getting started that money would be better spent elsewhere.
How do I choose a receiver and speakers?
A receiver has the least impact on sound quality, the speakers the most. Spend the least you can on the receiver while still getting the features you need. The hard part is choosing speakers, only you know what sounds good to you. Listen to lots of speakers to see what you like. Whatever you do, don't buy a cheap subwoofer, a good sub is essesntial for home theater.
I'm willing to read a bunch of technical articles about room acoustics, but do I really need to?
Not really, but you will end up doing it anyway once you get hooked

Your budget will get you a good base system that you can build from, future upgrades you will want to keep in mind would be things like room treatments and eq.
I would break up your budget like this:
Receiver: $300-400 (Yamaha, Onkyo, Denon)
Subwoofer: $400-500 (SVS)
5 speakers: $500-600
Remember, your surround speakers will see a lot less action then your mains/center, you don't need to spend as much on them.
Get your wire/cables from
www.monoprice.com, big box stores love to price gouge on them.
Internet direct companies are a great way to get a great speaker at a great price. SVS is popular around here:
http://www.svsound.com/, but there are many others.
If you have tools and are handy, building your own speakers is an option as well. There are many DIY designs that can produce excellent sound for a fraction of the price of buying pre-built.