possible ignition problem.

i have an 84 S-15 that runs great but when i start it up sometimes it doesn't start right away, i have to pump the gas or floor it. it sputters and misfires for a bit too untill it warms up it seems. also when i shut it off it sometimes rumbles and shakes for a bit.

i checked the distributor cap and there was corrosion on the metal contacts and the middle metal point so i clean those as well as on the white module which the cap covers, which looks a bit rusty. i have yet to check the spark plugs and a mechanic suggested i need a new ignition module. i'm going to check the battery as well to see if it needs cleaning.

any ideas on whats wrong or if theres more info i need to find out. thx.