How do you choose between Bluefin and Bazzite? Can you do any gaming from Bluefin, or is Bazzite a requisite for an easy functional setup for this?

The difference is mostly about default settings

Bluefin even includes stuff like built in propietary controller support and such

If on desktop I'd probably keep to Bluefin (Gnome) or Aurora (KDE) mostly because those have better defaults for it