I don't think "name recognition" means much. Employers know it's more about you than which school you went to. You might have a point as far as networking. Bigger school, more grads in the biz, more chance to network. That said, networking can work anywhere, at any flight school.
In any case, I don't think the advantage you might get in networking is anywhere near worth what you'd pay. Don't pick a school on "name recognition" or who has the best website or best marketing. Since your dad is paying for it, go check the place out. Then go check out some other places. Let us know what you think.