The odd wet weather behavior is a tip off that this could be possibly ignition related. How recently did you have a full tuneup on the car? Have the sparkplugs, sparkplug wires, distributor cap and rotor been replaced or at least looked at? Another thing you can do is look under the hood at night (make sure there it is as dark as possible) - if you notice any arcing anywhere on the engine or ignition system - could be a sign of misfiring or damaged ignition system.
As for the choke issue - it would cause similar problems on a carburated engine. Your car is a 2nd generation Camry with a 3SGE 2.0L inline 4 EFI engine - no choke. The 3SGE was also used on Toyota Celicas and other models - noted to be one of the most robust series of Toyota engines.
I would also recommend you run a good quality fuel injector cleaner - give the age of the car, even with the new fuel filter, could be some significant amount of gum and varnish in the fuel system. Make sure the air filter is in good shape and the airbox does not have any visible damage to it.
Another possibility are sensor and electrical issues - as like the ignition system, will act different when components are wet. Most basic one is the chassis ground connection to the engine - basically makes sure that the engine is at the same potential as the negative terminal of the battery. If that is not the case (you could use a decent multimeter to measure both resistance between the engine and negative terminal as well as voltage (mV range)) - you could have an uneven idle, poor acceleration, or stalling.
I would suggest a good tune-up first, if that hasn\'t already been done, then start working the possible issues in the ignition system, electrical, vacuum, etc. To start diagnosing it before the tune-up may cause more problems because you have too much variability to work with.