Hi ChelseaMom,
Welcome!
I have my children in a private gifted school. DD5 is in kindergarten right now.
We have been very pleased. Our dd is reading at a third grade level and able to do math at about that level as well. However, this school enables her to do this work without leaving her kindergarten classroom. For dd5 (who is rather young - a summer birthday) this has been a godsend. I know that others on this board have had quite a bit of success with subject/grade acceleration, but I am not certain that socially my dd could have handled it.
One other thing I wanted to mention is the peer group. DD5 is a quirky kid ... and may have had trouble finding kids who shared her interests. Or accepted her as she is. At the gifted school, an obsession with dinosaurs or rocks or pokemon is treated as the norm.
As for your other questions, have you toured the school? Sat in on a class? Maybe observed a whole day? Do you know any parents who currently send a child to that school? That might help you discover if the competitive nature is running rampant. Each school is different, I suppose...
