95 Saturn SL1

I have a 95 Saturn SL-2 with an automatic transmission and a TON of milage. It idles ruff at traffic lights like it wants to stall....and cuts out on excelleration, or as your driving at a higher rate of speed and let off of the gas....it sounds like it wants to stall....but kicks right back in when you step on the gas...also...when it's cold...it fires right up....but after it has been running and you shut it off...it's VERY hard to get started again.
Someone said check the oxygen sensor....any other clues or ideas out there???
Thanks!

Change your ECTS if you never have

here is the correct replacement, dont just buy one from a parts store, get it here or at a dealer so that its a brass tipped sensor
http://www.trademotion.com/partlocator/index.cfm?action=getLocator&siteid=715&chapter=DP8V00&appSectionid=3&groupid=10046&subgroupid=60344&make=31&model=Sl%20series&year=1995&catalogid=1

And clean your Throttle Body and IAC valve,

These three will probably cure the problem and dont cost much

Then Reset your computer, (Unplug battery or PCM B fuse for about 30 minutes, can do less but thats just to be sure)

I just bought my 95 sl at a dealer auction and the car was acting in some ways the same as you are describing yours. It turns out it one of the spark plugs was loose. and the wire was also loose. Since I replaced all plugs and cables the problem went away. You might want to inspect your wires see if they are connected properly to the plugs and to the coil packs.