Lowest Budget??

[ConKbot of Doom]

Each kid that was to participate had to raise $400 for our team if they wanted to go to the competitions. That is how we handled our cash. I managed to land Jacobs Engineering as our main sponsor again this year and get $10k. But most of our costs was travel, hotels, and event registration. We only spent about $500 on additional parts for our robot.
After the initial sign up, 60 or so kids going to 2 regionals, plus registration, the little bit extra for parts on the robot, it was projected around $30,000. But the team downsized to around 30, so it wasn't that high. I don't know what the final budget was.
And I would have to agree, having a good build group, and good advisors is definitely more important than having a ton of cash to throw at it.