if you're looking to hold onto the screen for repeated use, i'd suggest an aluminum frame. if it's a one off type thing, wood will work. mesh would depend on the artwork and how detailed it is. the more detail, the finer the mesh. you can make your own screens, too. i did that for years actually. but now, since you only need one, i'd say go to amazon. i hate saying that, but it's probably your most cost effective option.
I've got mine from Aamazon EEZGLOBAL 006431 screen printing machine. But before buying this printing machine i did a little bit research here and then finally take decision to buy.
All-metal construction. 1.2″ thick screen frames. Advanced electrostatic spraying and electroplating.