Yeah, to lose weight, you're gonna want to burn off as many calories as possible, meaning LONG 3-5 hour rides that burn off 2000-4000 calories. It'll take a month or two to build up to that level. Then if you can do two of these rides a week, you'll be burning off as many calories/wk as possible. Watch your diet to maintain a calorie-deficit and you can lose 1.0-1.5 lbs/week. This is the maximum safe amount for permanent weight-loss. Much more than this and you'll end up losing a lot of muscle-tissue, which will result in constant fatigue, loss of motivation, and eventual abandonment of the exercise programme and the weight will pile back on.
The idea is you want a sustainable and permanent change in your LIFESTYLE. It's got to be something you can keep up forever. As soon as you stop, you'll end up reverting right back to where you are now. So think beyond an August deadline.
As far as riding, start out with 100-miles/week at a steady pace. Then start mixing it up, doing shorter more intense rides on some days. And longer slower rides on other days. Work up to 200-300 miles/wk.