I would do the stairs in the same vinyl as the floors we did our baement stairs that were really old and they look awesome I rarely like real wood next to fake.

If it is for a relaxed lake house - I would lean toward painting them (I have used wallpaper on stair risers before and it is really easy to apply and can create a lot of impact) - you could also add an informal rug (Dash & Albert has great ones). If you paint them - make sure to do research on the paint so they are not too slick - esp with wet feet from the lake :) Sherwin Williams has a mix in for stairs that keeps them from being slippery - have fun, I think stair projects have such a high ROI

since this is a lake house, just paint them (and the banister too). don't try to make real wood and vinyl match, it rarely looks right, and staining is a huge pain in the butt. painted steps will be easier and will look perfectly fine for a "slightly imperfect" vacation home.

normally I'd insist on doing matching vinyl on the steps. but new vinyl can be a little slippery, so I wouldn't recommend that unless you were ok with also adding a runner. which I assume might be out of budget for this particular home?

Adding vinyl on the stairs added almost $2,000 to my costs, so yes, that is a factor. I’m also very concerned about vinyl being slippery and overall longevity of the product on stairs. So, paint! Black? Espresso? I like easy, and I like the idea of something out of the ordinary on the… vertical part in front of each step. What’s that called? What kind of trim goes in the corners on each side?

can we see more pictures? what style are you decorating? and I'm not sure what you mean by the trim at the corners. (if you're talking about the gaps, caulk them.)

I love all black (and black and white) for stairs, but that's a little more formal. if this is a lake house, are you going for more of a beachy theme? light/medium colors will be more appropriate. no to brown. people seem to think that's going to look like stained wood, but it never does. it just looks dull and flat.

remember that colors make a difference when it comes to maintenance as well. black stairs will show every speck of dust and hair, they'll need to be swept more often. white (or very pale colors) will show scuffmarks more, especially if people wear shoes indoors.

texture matters too. I suggest satin. gloss will highlight every little dent in the wood, matte might look dirty way faster.

if you want to do something different, consider wallpaper for the risers:

The existing pine 2x12 treads will not sand smooth or take paint/stain properly. The treads should be hardwood if exposed.