I am going to have to respectfully disagree with some of the other posters.
What I saw in the video was a *very* made, very ridable Chidlren's Jumper. Perhaps the other posters were looking for something that would go more like a hunter? I like this horse very much, and I particularly like how adjustable she was and how she's taking care of the rider. She looks to be a great first show horse for the jumpers, to build a rider's confidence and show them the ropes. Looks like she's also capable of advancing under the right rider as she can clearly handle more height.
$750./month is not outrageous for board + lease fee for something capable of doing rated shows. Show barn board in my area is at least $500./month, $250/month on top of that for an experienced show horse seems pretty reasonable to me.
For a pleasure horse or a local show horse, yes, it's a lot of money. Horses capable of qualifying kids for indoors lease for lots more.
If you like her when you ride her, and your trainer thinks it's a good fit, I say go for it. The great thing about leasing is that if it's not all that you expected or not working, you can always terminate the lease and go on to the next option.