There is one other organization that you can be part of without the expense of forming your own 501(c)(3) -- the Explorers. Part of the Learning for Life organization, Engineering Explorers is an educational organization intended to provide opportunities for learning about career opportunities in STEM.
http://www.learningforlife.org/explo...ing/index.html
I don't know anything about 4H, so I can't compare to that, but the Explorer program provides some real benefits to someone starting a robotics team. First, all your adult volunteers will register with Learning for Life and go through a formal criminal background check. I view this as a way to reduce my personal risk of allowing an inappropriate volunteer work with youth. Second, they carry liability insurance that protects leaders during Explorer Post events. Third, they offer Youth Protection training to adult leaders. If you create your own 501(c)(3) you will need to handle these things on your own. I wouldn't consider being a volunteer for a youth organization that had no liability and risk coverage for adult volunteers.
The only real downside to the Explorers program is that it requires you to be aligned with at least one corporation or government agency which "charters" the post. In our case, our corporate liaison is also our post advisor. We pay about $10 per person per year to be a Post.
Our local Exploring office would handle our finances for us (they are a 501(c)(3)), but we are lucky enough to also be an affiliate member of the Seattle Robotics Association, which is a 501(c)(3) that handles the finances for a few robotics teams in the area.
Whichever route you take, good luck and have fun.