You can find the casting numbers on the block near the bottom. You should not have to remove the starter to find them.
It does sound like you have an older set of heads. The early heads used press in studs with a rail or standard rocker depending on the head date. The standard rocker head has a sloted hole for the push rod like a Chevy the later rail rocker has a round hole both use the press in stud only the HP heads had screw in studs.
If they do not have 302 cast in the heads they are not 302 heads. Ford cast 289 in the 289 heads however they will work fine on the 302.
Look for a letter followed by a number on the block. C is 1960's D is 1970's and so on. The next number is the year of the casting and may not be the true year of the engine as some casting carried over.
Why are you thinking of pulling the
oil pan? What did you find in the filter that has you so worried?
Unless you found some metal or old bits of valve seal you should not have a problem. If you did you have something to worry about but you should have seen a BIG drop in
oil pressure as the car warmed up if not a noise when you first start it up.
When you change
oil on your car remember to always add oil to the filter before you put it on to help prevent a dry start.