I bet you need some budget to market the tournament itself so don't put all of it into the prize pool
Would be shame if only 5 people took part in the competition and you still have to give away $1000.
I would use some of the budget to hire a freelancer to make a good promo video of your game and some money for facebook or other social network promotion. Also if you are planning to release on PC and have keys/beta keys, I would suggest to send those for Youtubers. Personally I've found Keymailer to be very effective.
If your budget is $1000, the prize pool should probably be around $500 at max. Then again this all depends on how big your fanbase is. Although with the information given, I would use more resources to reach potential players.