The most likely cause of hard starting in wet weather is bad plug wires. When it is dry and the car starts, try spraying the wires with silicon oil. If the helps or solves the problem, you need new plug wires. Go for an OEM set. They are more expensive and harder to find (you will have to order them from someplace like IPD), but they are more reliable.

The green terminals in the distributor cap sounds like moisture is getting into your cap. That usually means that your current cap is cracked. Replace it with a real deal Bosch cap with brass terminals. Same as the wires, it will probably be 3X more expensive than a cheapo aftermarket knockoff, but it will be more reliable.

How long has it been since this car has had a thorough tune up ? It could be time.

Greg