5 year old Compaq desktop with Nvidia 8800 - Can I use any newer card in that machine?

My kid has a a 5 year old Companq desktop with an early model Nvidia 8800 in it. It has a somewhat upgraded PS from Thermal Take. If I was interested in just replacing the video card would any modern card that would fit in the PCI-E slot work?

What’s a good card for less $ 125?

Yes, but you need to check the power requirements against your power supply. This card is pretty popular.

Assuming power requirements are met, yes.