Which type of paint should I use for wainscoting?

I would use latex with a gloss because it is washable and will last longer.

I used High Gloss Rustoleum. It made my plaster walls look like wooden wainscoting with just the wood trim. I used this paint on all my painted woodwork.

Forgot to mention that I used Oil Base High Gloss Rustoleum. Wears like iron.

I would use BIN ZINSSOR primer first. It doesn't flow quite as well as latex but you will thank yourself for this step. Latex will bond to it and be washable. I had granite counter tops installed and there was a clash between them and the tile back splash I couldn't live with. A wise Home Depot lady employee at the paint counter introduced me to BIN ZINSSOR and I will forever be grateful.

When I want hard finish on a wooden surface, there is nothing like Benjamin Moore's Satin Impervo. I used on my kitchen cabinets and it holds up. It is a great enamel paint. It is more expensive than the big box store paints, but if it holds up and you don't have to repaint, then you have saved time and more costs! Priming the are first is also a good idea just be sure the primer is specific to the type of paint you are using. Latex is pretty, easy, and drys fast, but will rub off. Personal experience!

i have had really good results with a semi-gloss latex paint. Doesn't stop the dirt/dog oil, but does clean up very well with soap and water

Thank y'all for the help. I think I will do a comb of these things. Kids and dogs...never really home-friendly but wouldn't train them for the world.

Use a semi-gloss that can be wiped down. You can also buy child-proof paint at any home improvement store that is washable and more durable for kids and pets. All of the major paint brands have it.