Though there are probably white papers about this, let me give you a few suggestions offhand:
1) Learn the format for an actual business letter. You'd be surprised how few people know that kind of thing, and appearance can make a big different. Having some kind of team letterhead is very helpful, even if it's just a logo printed on top of a page.
2) Have details of your event in the letter, and invite your sponsors to attend! Make sure they know that you are an active team, tell them about your past competitions/events, and if you are a rookie, tell them about your plans for the future.
4) Proposal vs Sponsorship...
Now, am I correct in interpreting that these are two different things? Are you proposing the event to your team leaders, and separately asking community organizations for sponsorship? Be sure to get team leader permission first.
Other than that, just get it set, and maybe ask your parents or family friends who have experience with business letters if this letter is something they would enjoy recieving and would feel compelled to respond to either with sponsorship or with positive vibes. Welcome criticism.