I don't think I have run into a TV yet without buttons on it. Maybe some of the cheapest low end sets may have them removed. Did you check WalMart, Best Buy, etc.. to see what they have? I would forget looking for a non smart TV and just look for a good one in your size from a good brand, Samsung, LG, Sony, Vizio. 1080 resolution would be best if you can find something you like in your price range. Many of the 32 and smaller TVs are 720 which is not great and can have display issues, especially if used for a computer screen.
If you plan on using the built in tuner you might want channel+- on the TV chassis.
If you are going to need to change inputs you might want that on the TV chassis as well.
A smart TV pretty much requires you to use the remote so a dumb TV would be more useable without a remote.