Hi! Happy to share my experience.
I mentor for FIRST, and volunteer as a judge, field operator, or whatever is needed for the regional competitions. For mentoring I like to help the First Lego League (4th/5th/6th graders, whereas the other leagues are for older students). I think Dean Kamen's done an awesome job of motivating, coordinating, and empowering volunteers to make FIRST into an incredible organization. I can definitely recommend getting involved with FIRST. There are various levels - depending on the age of the children. FLL teams might not have the students doing their own outreach for sponsors, community involvement, etc. but the older leagues certainly do. At the FTC and FRC levels the teams are expected to be self-funded - and that doesn't mean parents covering the difference. It means they find sponsors, do fundraisers, etc. as well as build and program the robot.
For the FLL, the kids are young enough that it's doubtful they'd be able to estimate their team spend, find sponsors, etc. However, they're also not building a robot that involves cutting, custom parts, etc. - FLL robots are ONLY build with LEGO - not with metal. SO... that means the school can re-use the LEGO kits from year to year. That means, if you find some corporate sponsors (who might also contribute mentors, guidance, etc. along with LEGO kits) one year, they won't have to throw the same amount of money at the project the 2nd, third, fourth year. Of course, there will be some need for replacements - rechargeable batteries fail after a while, for example. Parts break, and disappear. But, generally, the kits should be useful from year to year.
I would invest in EV3 kits - NOT in NXT kits - if I were you. The software's better, the controllers are more powerful and more capable, and the kit's simply better than the earlier NXT kits were. For around $1000 US you could get 3 kits, enough to support a dozen students (four per team) - and that's not an unreasonable amount to ask of a corporate sponsor.
Hope this helps! Please don't hesitate to reach out if you have further questions.