Some experiences:
1. You'd better buy the dumbells with bars and plates, so you can adjust weights later. Don't buy fixed weights ones.
2. Usually 3 set for each exercise, in each set, 4-7 reps heavy for muscle strength, 8-12 for muscle size, 12-15 for definition, 16-20 reps in light weight for fat burning.
3. If you want to lose fat, the only best way is running or cycling or any cardio exercises, rather than just weight lifting.
4. If you want to bulk up, you need a lot more than just dumbbells, better go to gym, get a program. And you need eat right and eat more.
Just get a pair of dumbbells wouldn't help you a lot. And the most important thing, keep a consistant effort, 3-5 exericses every week, no shorter than 6 month. Most people quit at first 3 weeks, because it get less interesting, more painful, and no visible result yet. After 3 month, you will start to enjoy it.
Hope you will get what you want.