You should be careful about selling before you have a business license and such. Obviously this all depends on the country, state/province and city you live in. You should really research what is required to sell your product unless you wish to be shut down and/or pay fines and excess taxes. (A lawyer and/or accountant may be a very good idea here.)
Having someone else sell your goods may work, but you should still do your homework. You could get screwed over.
If you’re simply gauging interest, try to find ways to hawk your wares where you likely won’t be subject to regulations — like point #2 you suggest — and of course charity events like bake sales, church functions, or local fairs put on by small organizations, etc. If it’s starting to take off, consider talking with school administration about long term feasability (perhaps a poor chance, but it never hurts to try).
If you’re worried about putting down capital for a full shop, think small. What would it take to be a legally selling food truck? Even better may be finding a partner or two and splitting costs.
Or why do all the work yourself? Bakeries exist, so why not use their equipment and already established business connections? Apply or convince a bakery they need to hire you to bake and sell your doughnuts there.