A few points: first, if you're thinking of commuting regularly via bicycle, a second steed is a good idea. Personally, I would put fenders on the old 830, fix it up a bit, and use it as a secondary/rain bike. Then, given the length of your commute, I'd find a good older steel road bike (preferably with a double butted frame set) and make that my primary commuter. Figure out your sizing first, as others have pointed out.
Second, whatever you do, keep the rear brake. If there's one thing on a commuter you want to be a redundant system, it's the brakes. You'll be in traffic and will need to stop a lot. A second brake is always a good idea.
You can work on the bikes yourself if you're mechanically inclined (as you seem to be), but definitely make sure you carry a few tools for roadside repair. I'm of the school where I actually like to work on bikes, and there are few better ways to learn about them than to do a complete overhaul/rebuild. As others have said, it can be frustrating, but it is also rewarding.
As to the crazy point, we're not really crazy, it's just everyone else thinks we are. We're actually crazy like the fox, if anything. Commuting is fun on a bike, and drudgery in a car. But then, what else would someone on a bicycling forum say?
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