Becky, It is a tough decision, but for me my first big tool was a table saw, so I would have to say, a table saw. And if you could, try it out first. I have a contractors saw, I understand you have restricted space, but try the saw out if possible, a friend of mine has an old sears craftsmen bench table saw and it makes me nervous when I am at his shop and we have to use it. Just make sure it is a solid saw. (if you decide on a table saw). My next tool for me was the tougher decision, a band saw or planer. You are right you can plane down the thick boards, but it always bothered me knowing if I only had a band saw I would not be throwing away another board, because you could get two useful boards out of one, by re-sawing it on the band saw then planing it. I bought a band saw first, then I bought the planer. I know I have rambled a bit, but It is a tough decision, good luck and be safe.
Mark