I've done some searching so I hope this isn't something that is easily found.

I live in Florida so it doesn't get very cold... think like 75-90 right now 24-hours a day. I bought this car about three months ago and everything is stock (1985 GSL-SE), the previous owner took good care of it and brought it to be worked on whenever it had any problems, except towards the end apparently. All the fluids were changed regularly, I've replaced the rotor, cap, wires, plugs, did an oil change, replaced the air filter and heat riser tubing. It stalls if you don't keep it around 1500-2000 RPMs when first started for about 10 seconds if it hasn't heated up yet. The whole car sort of shakes left-to-right no matter where I've got the pedal until it's heated up. It sounds really sputtery. As soon as I drop it into gear though it seems fine, like a bit of stress on the engine solves the problem. I do know that the exhaust system leaks a little bit, could this have anything to do with it? I've quickly looked over all the vacuum tubes and didn't see and breaks. I almost exclusively put in top-tier gasoline... I think that's about all the information I can give.