Painting - Painting stair treads and risers

I have seen some stairs that have been painted........we have a townhome built in 2002 with just normal stairs and yucky carpeting. We don't really care if the stairs look like hardwood or if they're just painted.......we just want the carpet to GO! Can't afford to put nice hardwood there.
My questions are: What kind of wood is under that carpet, more than likely!? Can I sand, fill holes and gaps, sand some more, caulk and then paint brown on the treads and white on the risers (I KNOW this will take a TON of time)? Is is possible to stain the treads or is the wood yucky?
IF I can paint, what kind of paint and sealant over the paint should I use?
THANKS!!

You want carpet on the stairs. Chances are very good that the "wood" under the carpet is not anything you want exposed. The majority of housing over the past 30-40 years has relied on carpeting to cut expenses.
The only way to know for sure is to pull back some of the carpet.

Bobf is right, its probaly cheap-o pine. But it can be painted if wanted, but usually wood like tis is filled with knots and dings, and used under carpet for this reason. But if you still go for it, use a latex boding primer, like Zinsser 123, and then apply 2 coats of porch/deck/floor enamel. Good luck.

What about the front edge of the treads? I notice when I come down the stairs, that's the part that takes all the weight and roughness.......how can I reinforce this or help it NOT splinter or chip??
Thanks so much for your help!

The front edges should be strong or tough enough to stand any kind of weight. It is just an aesthetics issue, will it look good or not.