[MENTION=41805]retro[/MENTION]-Grouch and [MENTION=28167]dedhed[/MENTION] have a pretty good lists. It's about what i've done on BSO tune-ups.

I would try to replace as few parts as necessary. Minimize the cash outlay. Get a take-off RD (A-series or Tourney) don't spend more than $5-10 for it. New brake pads can be had super-cheap as well, and help if you're trying to reset a badly-adjusted set of brakes.
Probably a new chain, as well, again don't spend more than $10. I have been able to get KMC Z-51s for $8 from the co-op, but the $10 BELL-branded chain from WM will do in a pinch.

If you have the time, you could probably find some nice thick 'cruiser' tires for cheap, other wise figure $40-50 for new rubber ($20/each) and more like $75 for flat-resistant.

All the tuning in the world also won't get over that really crap FS frame. Some of those are so badly designed that the only way to make the rear suspension not mess up the driveline is to bolt it all down so it doesn't move.

A quick look through my local CL turned up a decent selection of bikes for less than $100, some old GT and Raleigh MTBs, and some 7-speed cruisers and 'comfort' bikes that might hold up better.