Welcome to the forum. Congratulations on your weight loss. IMO, cycling can be a part of a healthy lifestyle. How much of a part is, of course, up to you. In other words, you could decide to cycle for exercise, for transportation, or just for leisure. You can, of course, built up to rides of 12 to 16 miles round trip, and much further, if you put in the time.
Now, as to the dreaded W question, my recommendation is to stay away from Wal Mart and other department stores. They are an abomination, and the bikes they sell are cheap, but they are not good values. IMO they could wind up costing you more in the long run than if you just bit the bullet and bought a decent bike to begin with. That isn't to say you can't get a decent bike for $250, but unfortunately you can't get a decent new bike for $250.
If you have any followup questions, feel free to ask.