what should I look for as far as functionality. There are parts I know I can replace but what are the small problems that aren't worth fixing?
Look the outside over well if it has not rusted or been beat it is worth looking closer. I look for brand names I recognize. You will know the things that you want like heavy barrel or target sights and stocks.
Take a light and look into the bolt face, note the position of the firing pin then look at the corresponding area of the breach face for firing pin impact from dry firing easy fix with a inexpensive chamber iron. Next take a look at the extractor system. Does it have one, are there any obvious missing/broken parts, this is common extractors are easy to replace and you might just do it anyway. Most have a ejector of some type can you see it and is it intact. Some Marlins have a ejector that is held in by the barrel/receiver. To change the ejector the barrel needs to be removed on some the ejector is riveted from the inside of the receiver with a special tool, so this is the type of part that is a deal breaker. So look for the ejector. Take a dummy round and check the action/magazine tube. Some tubes are two piece and the inside may have a dent or obstruction and the outside look fine mag tubes can be a deal breaker. Be careful about missing mags or damaged tubes so using a dummy round in a tube fed will tell if it is usable and the lifting parts are working and will it strip and present the round from the mag.
I don't pay much attention to dirt. If the owner will let you, use a dummy round and dry fire. Does the safety work!