Advice on my new winter beater

I just bought this 1989 Trek 800 today for $30 to be my winter commuter. I plan on replacing the chain, cables, housings, and greasing it up. Then possibly getting some new tires, maybe studded even.

Here is the fact sheet. The 800 info is on the far right. The crankset is a Shimano Exage Country 48/38/28 Biopace w/ sealed BB.

This was a craigslist find and my friend lived near where the bike was. I had him pick it up for me. So I didn't have a chance to give it a once-over.

Here is my question: It turns out that the bottom bracket is probably shot and the cranks wobble back and forth. What do I do? I have never worked on a BB (or a hub) but I can do just about everything else. Anyone have any advice? Did I buy a lemon?

PS: I took the pictures after I began to remove the pedals, straighten the seat, and clean it up a bit. I have broken the remainder of the pie plate off and polished everything up as best I could since these were taken. I have spare phil wood platform pedals to put on instead of the plastic ones it came with. Also, I know the bike is a bit small but I think it will do the job.

PPS: When I went to tighten up the cheap plastic brake levers/shifter mounts they came apart when tightened. If I replace the brake levers (I have spares), how do I go about remounting or replacing the shifter levers?

EDIT: Looks like this will be a $200 project what with the tires and all. Oh well. Probably worth it in the end. That isn't counting the cost of all the tools I will acquire in the process!