Well good for you, for trying to make sure you have all the details and information worked out before adopting a pet mouse! That is so good to hear.
I have never had mice before (just rats and gerbils) so as far as food goes, I am not quite sure. I know that lab blocks I have seen in pet stores usually say "rat and mouse" so I assume that works fine for mice in addition to rats (although I order a different type of lab block made for rats from Harlan Teklad), but as for seed mixes, I do not know if mice people use seed mixes or not for their mice. I know that seed mixes from pet stores are a no-no for rats, but that might not be true for mice. I know that lab blocks will always give your pet much better nutrition than seed mixes though, which can have a lot of fillers and junk in them. I would lean towards a good lab block actually.
And yes, a multi level house would be wonderful for your mouse, for climbing and so forth. I know there are some mice housing options that are single level but I have seen mice owners add all kinds of boxes and toy huts, ladders and so forth so their mice can still climb and exercise. Of course you need to also make sure your mouse has a good exercise wheel in his house, as mice LOVE their wheels!
As far as vet bills go, you do not need to have any kind of membership set up. It can be an "as needed" thing with a local vet. If your mouse is eating, grooming, playing and has a nice coat and no red flags such as a wet nose/tail, lethargy or any of the signs of illness, you should be fine. If a medical issue comes up, you can just call your local vet and bring him in for a check up.
Make sure you have a good local vet that specializes in small animals. They are usually referrred to as exotic vets. These vets normally treat pets like mice, rats, gerbils, etc, plus birds and some reptiles. My exotic vet does not even see dogs or cats, just other small pets. Hopefully you have a local vet you can look up so you know you have someone to consult with if your mouse should ever need medical attention.
I hope I did not give any incorrect information since I have not had mice before, but I was just trying to give some general tips on small rodent care based on what I know from having gerbils and rats. If anyone wants to correct anything I said, please do so!
I do not blame you for falling in love when your mouse touched his paw to the glass....ahhh, what a wonderful moment! Sounds like a perfect match.
I hope your parents see that you are obviously a responsible and caring "adoptive parent" for this mouse and that you would give him a good home. I hope they let you bring this little guy home before someone else gets him. Good luck and keep us posted!
P.S. Feel free to do lots of internet research on mouse care. There is tons of good information out there.