+1 Not the best choice for a commuter. You might be better off with an older rigid mountain bike, that can handle wider tires, and take a beating. Around here, you can find good ones for $100, sometimes less. But since you have a free bike now, you might as well start with it and see how it goes.

Do a search on rust, oxalic acid is the best thing for chrome. It doesn't take much of a set up, I did a fork last week (on the Lotus below) in a small kitchen trashcan. Anything abrasive (like steel wool, etc) will destroy the chrome while removing the rust. I found out the hard way.

Rim tape, tubes and tires can be found at low cost.

You can get a set of replacement cables (brakes and both derailleurs) for $5 at Walmart. If the bike has been sitting a long time, it probably needs cables as well. Ditto brake pads, which you can also find cheap at Walmart.

You might want to contact a bike flipper in your area. You can probably pick up used parts (seat, wheel, that kind of thing) along with some maintenance assistance, from a flipper. Easy to spot flippers by their ads on Craigs List: "bike just tuned up, ready to ride, replaced bearings, new tires,...). If the C/L poster did the work himself, he is probably a flipper.

You should be able to fix the bike for $50 to $75, if you do the work yourself. It will probably be $200 +/- if you pay someone to do it.

I have $55 in my 1984 Lotus below, including the $16 purchase price. But I buy most of the supplies in bulk (example, $3.50 bar tape). So your cost would be somewhat higher.