It's really hard to say without seeing it what it needs, but at a minimum I think you should get a new chain because you said it had surface rust and, unless $12 is going to break you, you don't want to ride around on a rusty chain. Also new brake pads, the old ones are probably hard and/or worn. And just spend the 5-$10 for new grips. Also get a bottle of thin lube, like tri-flow or pro-link.

You ought to take the thing apart and put it back together with new grease all around, but if you don't want to get that into it the above parts will help a lot in terms of performance and safety and will cost probably less than $40 total. Then another $5 or so for a little thing of lube and put a little on every moving part of the derailleurs (wipe off excess of course), put a little into where cables go into housings, put a little on the shifters' moving parts... stuff like that. It's hard to screw up lubing. If you lube something that doesn't need lube it won't catch on fire.

Give it a good cleaning first, of course. Just a damp rag if stuff isn't too bad, if there's greasy messes everywhere some degreaser or simple green... If the chainrings and cassette aren't too worn then your new chain will work great with it all (wipe off the excess packing lube on the chain- but no need to remove it, it works fine to keep the chain lubed for many miles). If the tires aren't cracking and stuff you sholdn't need to worry about those. Ride it like that and someday if you get the notion do stuff like relube the hubs and what-not, but that can probably wait.