1. Based on how long this bike has been sitting I'm sure I will have to completely tear it down to get it running again. I'm pretty mechanically inclined but motorcycle engines aren't my thing. What are some options for having the engine rebuilt? Any particular shops that people have had experience with?
I wouldn't bet on a total teardown. First things first- make sure that:
a) the engine turns over (pistons/rings not stuck from rust/condensation) Check your compression. Check for spark. Check for obvious leaks or an obviously blown head gasket. If none of these are present, hold that 'teardown' thought.
b) Check your gas tank. Might want to try to start the bike on a bottle for the first time if the tank was stored full of gas (now varnish) or if it was stored empty (and now rusty). Check around the bottom seams and the very top for bubbling paint which will tell you if you have tiny pinhole leaks from rust eating its way through.
c) Check your carbs. If the bike was stored properly with the carb bowls drained, they might not be full of varnish and other deposits. Honestly, they're still likely to have little blockages etc. The tiny passageways clog so easily. Best to do a clean, but why not attempt to start 'er anyway just to check compression and see?
2. What are "common" problems for these bikes (oiling issues, city overheating, etc.) that I should know about now?
These bikes are pretty burly. To overheat in the city is possible, but unless you overbore your cylinders, it's fairly unlikely. More 750 owners can chime in on this. I don't want to start an 'oil thread' but you want to be careful of anything that may make your wet clutch slip. Your are in luck, 750s are fairly tolerant bikes and will handle a lot of abuse.
3. Are there any parts that are practically impossible to find?
You are, again, in luck. parts for your 750 are available in a lot of places from a lot of retailers.
650s are more my thing, but I hope that helps you get an idea of where to start from. Lars is right on. You're looking at new cables and all new fluids, but your bike will be much happier for it. Before your first start, I'd recommend turning the engine over a couple times just to get some lubrication on the moving parts before they have to see any kind of appreciable (above, say, 50) rpms... She's had a long nap. Wake her up gently.

Best of luck to you, bringing a bike back to life is a beautiful thing.