I went to boarding school, there were kids who loved, hated or just accepted their lot. I guess I was in the last category. It definitely "formed me" into being independent & many would say "extrovert". the education however was excellent, & I was made to keep up, which for me was essential.
It was made up of rich, army, overseas & basically decent income families, but not a mega reputation school either. So no real snob value.
had I gone to our local comp, (at the time one of the biggest in the UK), I would have failed, rebelled & become a nightmare teenager ! It's easy to see that now, obviously no one could have predicted that at the time.
my brothers also were sent to boarding school, so I would have been alone at home anyway. but I do agree with the no "local" friends remark earlier. I had none.
I would have liked my DD to go to weekly board private school, her father saw no need, & didn't want to pay, altho we could have afforded it.
It was the worst decision we have ever made. she ended up dropping out with all sorts of horrific behaviour...
What I don't like about your situation is the offer to pay only for this one school option? it seems like a status issue, & not what is necessarily best for the DD. However I would definitely go & see, weekly boarding is a great compromise (she can stay at w/e if there are activities/sport if necessary)
& know that if she absolutely hates it, she can leave.