All US nonprofit organizations have received their formal 501c(3) tax-exempt status through a formal application process, which includes having a board of directors in place.
It's isn't a bad idea to ask for their letter with their formal 501c(3) tax information, as this is what individual and corporate donors must submit for their own tax purposes if they are hoping to deduct nonprofit donations. This is a very common document for nonprofits to supply to donors. The reason why you'd like to have a copy of this is so that, if you do get financial donations or big-ticket items, you can provide the person who gave you the money/item with an acknowledgement that the donation went to a particular nonprofit. There are a lot of requirements in order to actually take advantage of charitable contributions at tax time (high level overview is here
), so not everyone will care about this, but it is still nice to have as an option for those who do.
As an aside, I agree that choosing 1-2 organizations is plenty given your target fundraising goal. When you notify these organizations that you plan to pass along the proceeds, I would get them involved in helping you promote the event, whether it's on their Facebook page, by putting up flyers, etc. This sort of thing is a lot of work, and its much more rewarding to have a good turnout rather than just a couple of people. Good luck!