Moe, if you want the absolute most conservative way to go about cleaning and caring for this rifle this would be my advice:
1) disassemble the rifle. Use a proper set of hollow ground screwdrivers, a padded (rubber or plastic) mallet, and brass punch tools. Leave anything that is screwed into wood in the wood.
2) oil everything thoroughly using a penetrating oil. Kroil or something similar works.
3) clean the surface thoroughly with an oil rag. Get as much surface grime off as you can. You don't need to be aggressive.
4) For any rust spots hit them (gently) with some 0000 brass wool. You can also use a copper chore boy pad but make very sure it is the actual name brand and 100% copper. Cut a corner off of it with some scissors and make sure the metal is copper through and through, you don't want to use the copper-plated steel crap. Point being, DO NOT SCRUB WITH STEEL. Steel on steel is how you damage finish.
5) For anything really stubborn use a flat copper or brass scraper and attack it from the side. You can easily make one by flattening a brass rifle cartridge with a hammer and then filing the end to match whatever shape you need.
6) Don't do anything to the stock. Just leave it alone. You don't need to oil it, "feed" it, etc. If it has visible dirt and grime on it give it a wipe down with a damp (not wet, DAMP) wash cloth. If you need to do anything beyond that ask here.
edit: clean the barrel per normal - brass or plastic bore brush, your choice of patches, clean it chamber to muzzle etc.