I am wiring a basement for ceiling lights. I have not purchased fixtures yet and we want submerged lighting. My basement is rather small and I have decided to put up 8 fixtures and they will be switched on and off with (2) 3way switches one at top of stairs one at bottom. They breaker panel is new and has lots of expansion roon. The panel is within 20' of the switches and lighting. What size/type wire would you recommend? What size breaker? And can these 2 switches handle all eight light fixtures or what size fixture/bulb can they handle?

I'm assuming that you mean recessed lighting an not submerged (unless you basement floods a lot ;) ). You can use 14-2 NM-B (romex) with a 15A breaker. The cable should be run through holes in the joists when perpendicular or stapled to the side when parallel. The cable should not come within 1-1/4" from either edge of the joists.

The maximum size and type of bulb is determined by the fixtures used. There is usually a label on the fixture's can that tells what bulbs and trim can be used with it.

Most standard 3-way switches will more than handle 8 fixtures, however if you use a dimmer switch you have to make sure that you get one that is rated high enough. Many dimmers are rated at 600W, but you can get higher rated ones. Just add up the wattages of all of the bulbs.