I would like to install a light over the shower I installed in the basement but I do not know what type to use.if I first run the source through a GFCI can I use a regular recessed light fixture or does it need to be one that is waterproof or something.

You can use a regular 5" or 6" recessed can and a shower trim.

It does not need GFI protection, unless you want it.

Read the light fixture's manufacturer's instructions.

Most require GFI protection if installed in a shower or above a tub.

Most require GFI protection if installed in a shower or above a tub.Seriously?
I have never seen this in all my years. If you can find something please post a link. Now I am curious.

I have however seen it on bath fans when installed over tubs. Most manufacturers DO require GFI protection in that case.

As that may be the case that recess lights may not require GFI protection any longer, better to direct any installer to read instructions.

Probably with the use of nonmetallic trims, etc. manufacturers no longer state that it is needed.

There is not nor ever will be a home I wire that has a shower light without GFI protection. While the code lists minimums and maximums,exceeding the code is wise when reasonable.

Ans as always, check with local city, county, and state codes for changes and additions to the NEC.

I understand, for example, Washington state requires GFI protection for shower lights regardless of what the manufacturer states.