What's better: lots of reps with low weights, or fewer reps with heavier weights?

I’m pretty new to strength training. My goals (unsurprisingly) are to build muscle and burn fat. So what’s better—using the heaviest weights you can and doing fewer reps (approaching or achieving muscle failure), or doing lots of reps with lighter weights? And why?

Any other strength training advice is very welcome!

Bonus points: I overworked my quadriceps muscles and they hurt like hell. What can I do that won’t tax them at all until they repair themselves?