i-can-do-this,
There are treadmills that has shock absorption built into them. They're more expensive than the usual ones, but I have tried them. They're really nice to use. When you walk, the floor of the treadmill moves up and down, according to your weight. Feels like you're walking on grass. Maybe if you do decide to shop for a gym to work out at, check the treadmills. If they have these type, then you would be better off using these, to reduce the impact on your knees.
Swimming is another great way to get started. Swim a lot back and forth, do it for a while, until you have lost half the weight before running. That way, you'll be at a lighter weight. Less stress on the knees.
As for the coke, I totally understand where you're coming from!

I used to be a Diet Coke/ Diet Pepsi addict. I stopped drinking it for 3 weeks, and recently, at a birthday party, I drank some, and it was too much for me. Didn't really like the taste. Pepsi shocked my taste buds... There's so much sugar in that stuff. When you drink it all the time, it doesn't seem like a big deal. But after a while of not drinking it, you'd be surprised at how quickly your taste buds will say "whoa, Nelly!"
Anyhow, as for your knee issues, I would personally recommend that you do other exercises where you can take the weight off your knees. Bicycling, swimming, upper body weight training, ab training, etc. I would recommend that you should try to lose as much you can doing those things.
When you have reached the point in which you cannot lose anymore, then go for the treadmill, but try to use a shock absorption treadmill. But maybe you should check with your doctor first, and see if there were any supplements you can take for your knees. Calcium for bones, and something for the ligaments.
My back and knees used to hurt occasionally. But now that I have lost 20 pounds, there is no pain at all. It does make a difference.
Best of luck,
George