I know you said price was an issue (believe me, we've all been there), but not sure where you might be with that. My advice would be to use a local bike shop (LBS) because their help in fit will be very valuable. Most of the good brands like Trek, Felt, Specialized, Giant, Kona, etc., will have good solid fitness or hybrid bikes in the $400 range right now. They may, also, have a used bike or two around that you can get cheaper. I started with a used Trek 820 mountain bike for $50. I added new tires for $50 and had the LBS do a check up for $50 and had a great bike for $150. My son is still riding it as a commuter in college. Going to a local LBS and staying with one of the standard brands will get you a good bike and save you a lot of trouble in the future.
As far as losing weight. The important thing is to get out and ride and watch your diet. I've read where losing weight for cyclists is 80% diet and 20% exercise. I believe that. I think you diet to lose weight and you ride to be fit. I know it's not quite that simple, but I think it works that way for most. At first, you'll lose weight just because you're on the bike, the longer the better. It'll get harder to lose unless you also lower your calorie intake.
Since my doctor convinced me to start riding 6 months ago, I've lost 42 lbs. Riding has become addictive to me, but I've not felt this good in decades. You can do it too. Just search through this site for the many inspirational threads about those who've lost, sometimes, 100's of lbs. With a bike, it can be done, and done with a lot of fun.
John