Please help me. I'm analyzing my 1990 Miata. I need to find out if my fuel system is

[shfreezer]

bad or my spark plugs..? My car has problems starting up or doesn't even start up at all sometimes. When it starts up I have to keep giving it gas because it might die out and it also has a shaking and crazy motor sound to it. It's really rough starting up and sounds like it's only got 3 pistons running. After about 5-10 minutes of giving it gas, it will get to normal and the engine is normal. I checked the spark plug wires and one of the wires has oil on it so there isn't too much of a spark on that plug. My friend said that ya, my engine will be normal after about 5-10 minutes because even though it had a rough start, the oil is now hot and the engine can be normal and the car can drive normally. It seems that the car does this every morning or on cold days or rainy days. Could the car NOT start (or have trouble starting) if ONLY one plug was oiled or has oil on it? Could this be the case? I'm trying to see if I only need to change the gasket or is my fuel system dirty or bad?