my 88 Lincoln town car has trouble starting?

after sitting for over an hour or so my lincoln will start right up after i turn the key. however if it runs then is shut off and i try to start it up again it will just try to turn over and will just keep doing so until i give it gas and i have to hold the pedal to the floor and it will start to catch and sometimes will take up to 5 or 7 tries before it starts up and then when it starts the RPM's seem to flucuate for a bit and becomes steady. also when i give it gas it hesitates to go for a sec and in some cases stalls. . . its only got 87,000 miles on it. please tell me what you think ive heard everything from fuel pump and filter to a solenoid

This exact thing happened to an old car of mine right before it died. I'd have it checked out ASAP.