It sounds like you might be participating in a tournament that consists of more than just running or track events? If that is the case, and you will be competing in other sports and activities (especially ones that involve contact with other people or quick, lateral movements that involve fast right and left twists and turns, then the kind of shoe you need might be a bit different than if your tournament was only running events).
It sounds like a pair of wide, thick soled, and sturdy shoes are your best bet. You will need something that will withstand not just repeated beating when you run, but you will need a pair of shoes that do not lose their shape easily and offer some cushioning, padding, and protection when involved in contact. Furthermore, if you are participating in events and activities in which you will be making quick lateral movements or jumps (i.e. think movements similar to those involved in a tennis match or soccer game in which the player must jerk back and forth at a moments notice) then you will want to think about having enough cushioning to protect the impact on your joints (especially your knees) and a high enough heel so that your ankles are protected if you have to twist too suddenly, or over or under pronate when you turn. Plus, a pair of shoes with significant stability will last longer, and be a better purchase for the money.
A lot of fantastic running shoe brands make sturdy, stable, supportive, and durable shoes. Mizunos, Brooks, Asics, and Saucony all have great options. But because you likely will be doing more than just running, you can venture out a bit from the typical running shoes and try out Nike, Adidas, and New Balance. Having this kind of flexibility will give you more room to find a pair of shoes that more closely fits your budget. I advise going to a running or athletic shoe store and work directly with a sales person there to help you find a shoe. (These sales people are usually pretty skilled at helping you find the right fit and knowledgeable about which shoes are best for which activities.) Once you have found your preferred shoe, if the price in the store is too high, go online and see if you can find it cheaper.