I used a points/rewards system with my elementary grades 5 and 6, where teams could earn points and as they reached different levels, they got ice cream (50 points) and then pizza (100 points). It worked well, encouraged participation and lent excitement and such, but it definitely hurt me in my wallet (all told, I probably spent about 300k to 400k won. I don't mind spending some money on my classes, but that was a bit excessive.
My brother-in-law suggested that instead of a direct reward, let the points translate to chances in a raffle for a big prize; the more they participate, the higher probability that their name can get drawn. This could actually work out better, as there's still the randomness that gives a chance to lesser-ability students, and also the tension and excitement in the students might ramp up even higher.
What I'm thinking of is using this system, keep it contained for each class (1-1, 1-2, and 1-3 each have separate drawings) and doing the drawing once per month. As I'm starting in a middle school, I think I'll use gift cards to coffee shops or paris baguette or something as the prize.