If you decide to replace the carb, I recommend replacing it with a Weber carb rather than installing another stock carb or doing a rebuild. I tried for years to get my stock carb to work acceptably and it just got worse and worse until the car was undriveable. Guide here:
87-90 Tercel Weber 32/36 DGEV Swap Guide
There are several vacuum switches that are a part of the original carb system which are prone to failure, plus the carb itself has an issue with allowing un-metered fuel in due to a teflon coating that dissolves in gasoline over time

. This could be the cause of your surging problem if extra fuel is going into the mix and the computer is compensating by adding more air via the bleed valve, effectively the same as pressing down on the gas a little.
There are several pollution control and air bleed widgets that don't activate until the car warms up. The EGR valve and EGR vacuum modulator would be the most severe - if they were opening at idle, the car would barely work once warmed up. Also the throttle positioner system can cause surging if it decides to hit the gas at inappropriate times... on my '89 it had decided to give full throttle all the time until I disabled it. In my case, one thing after another failed on the old carb system until the car decided to idle @400RPM (which it can't) and became undriveable. It worked ok when not warmed up, despite all of the severe problems once it did warm up.
I've personally never had any ignition related problems on my car, which still worked (poorly) with all original plugs, wires, coil, alternator when I bought it @130,000miles. They could be a part of your problem, buy my bet is on the carb as the main culprit.