When I used a bike for commuting, I would buy bikes with 100% expectation that they would get stolen within 6 months (I've had over 7 stolen from me). So I would usually buy a bike second-hand for the equivalent of about 40 USD. So long as it had straight wheels, working brakes, a maintained chain and gears and a solid frame, I was good to go. (Cables / tyres / tubes I could replace / fix myself. Other repairs wouldn't make a lot of economic sense.)
A heavier bike is slightly harder to push up hills and harder to accelerate, but if fitness is your concern, it's immaterial IMO. Spending a lot of money on a lighter bike strikes me as a waste of money. Actually, spending more than the equivalent of 200 USD on a new bike would strike me as foolish.
Of course, if your the sort of person who would only ride in a circle from your house, or your car after having driven your bicycle somewhere, then feel free to ignore all my words of wisdom.