Beretta has hard starting issues

I have a 1994 Chevrolet Beretta with a 2.2l engine. Ever since I bought the car 4 months ago I've had a hard time getting it to start with the engine cold. It doesn't matter what kind of day it is if the engine hasn't been run for more than 3 hours it will have a hard time starting. It's even worse on wet days, but it will start. To get it to start I have to hold the gas pedal to the floor for about 10 seconds and then it will finally start and the engine will stutter for about a minute while it's jumping around in the engine compartment. After that it chills out and runs like brand new. I don't really know what to think about it. As far as engine repairs I have replaced the fuel pump, fuel filter, catalytic converter, head gasket, and it has new spark plugs and the right 5W-30 oil in it. What could be causing this issue? Before I bought the car the previous owners let it sit outside for a couple years so I don't know what could have possibly gone wrong in that time. This is truly irritating and I'm afraid that it will just fail to start one day. Could it be something electronic or would it have something to do with the fuel system? Any suggestions? I have a very limited supply of money so I can't be spending a ton on having it tested at a dealer or anything.