Hard start and rough idle

HI everyone I just bought my first car a 92 toyota camry 4 cyl manual transmission. Let me fist give you some information on the car its self. I bought it in June of 2009, the older laddie that owned it had put a used 130,000 mile engine in it after she had run the oil low on her other engine which had around 200,000 miles on it. Then she put a new radiator, distributor, alternator and a fuel pump in, all of which she did in the last two years. When I bought it the one thing it needed was new back struts. So we drove it home on the highway bouncing all the way, they are really bad. The other thing it needed was a new coolant temp sensor which I replaced. Now that you have the back ground info, here is the problem. We got it home fine and parked it, the next day I went to move it and it would turn over but not start, after turning the key a few times it would start but then stall/die immediately. After doing this a few time the car would start but it would have a really rough idle, RPM at around 400, if you hit the gas right away to move the car it will stall out again. You have to wait about 3-5min with the car running before you can do any thing with the gas. After i revved the engine the rough idle subsides a little then after driving it for a short distance the rough idle is almost not their anymore. After you get the car started and have hit the gas once, restarting is easy if you do it instantly. I like to work on cars so please don’t just tell me to go the the garage I would like to try and fix it, but at this point i have no clue what to do. Any help would be great.