Not sure what you need to know. Here are few tips:
Steel wool will remove rust and also chrome. Brass wool, should you be able to find it, won't remove chrome. If you want to get serious about rust, read up about oxalic acid on this forum. But don't get oxalic acid on any aluminum or zinc plating.
What's the problem with the chain? I see that you have a chain tool, so you must know what what you're doing there, at least minimally. If the chain is a little rusty, it can be oxalic acided too. If it's very rusty, replace.
Grease is for bearings, seatposts, stems, maybe cables, and anything with threads.
Oil is for chains. (WD-40, by the way, is not an appropriate lubricant for any of these situations, as it melts grease and dissipates, leaving you ultimately with no lubricant).
If the bike has not been serviced in a while, you should open up everything with bearings in it: headset, bottom bracket, hubs. Degrease everything thoroughly. Replace pitted or rusted bearings. Pack everything with lots of lovely grease, reassemble, and re-tension the bearings.
Be careful with degreaser and strong detergents: they can destroy paint and decals, plus be absorbed by your skin and turn your liver into a bag of maggots. I should know.
Aside from the freewheel (which uses a special splined tool to remove it), most everything on an electro-forged Schwinn (Varsities, Continentals, and a few others) can be serviced with regular tools (e.g., wrenches). In order to service the bearings in the rear hub, you'll need to get the freewheel off. You can order this tool or buy one from your LBS or take the wheel to the LBS and they will remove it for a small fee. When you want to reinstall the freewheel, just grease the threads on the hub and spin the freewheel back on. Reinstall the wheel and ride the bike up the driveway, and the freewheel will tighten down on its own.
The left-side pedal and the nut that holds the crankset together on the left size of the bottom bracket are LEFT-threaded (counter-clockwise turning tightens them).
To get the stem loose, unscrew the bolt about five or so turns, then whack it with a rubber mallot (not a hammer!)
Those Schwinns used weirdo small-bore cable housings, making it slightly difficult to retrofit with modern housings, so preserve the old ones if possible.
Eventually you will want to true the wheels. Long before that, remove the tires and rim strips and put a drop of oil on the head of each spoke nipple. Let the wheel sit for a few days. Then, when you go to adjust them, the nipples will turn instead of rounding off or breaking the spoke.
Welcome to the C&V club. You've picked a good bike to start on. Here's your new bible: http://www.sheldonbrown.com
Others will suggest other useful and legitimate resources. Of course, ask any question here, and the mostly-cheery people will mostly be glad to help.