Working at a startup could certainly be a highly relevant opportunity for you, given that creating a startup is your goal.

As for the research, definitely go for it as long as you know what type of research you want to do and why. The importance of your research skills depends on what industry you are in.

Ok, so you want to do “more ambitious things” and “things [you] do care about”, you say it’s been hard for you to come up with new ideas.

OP, do you… have a better idea in mind? If this website for your hometown’s high school is the only idea you’ve got, just focus on that. Worry about leaving for a better idea once you actually have a better idea. If you just can’t stand your current idea, however, then give the website to someone else to keep building/maintaining (such as school staff or otherwise someone more interested)