Yes to the case, no to the screen protector (depending on your phone model).
Most phones have some version of gorilla glass or ultra scratch resistance glass. If you’ve got this, you probably don’t need a screen protector. Your screen is probably harder than any screen protector you can buy, and that protector will scratch, and now you need to replace the screen protector to get rid of the scatch, over and over again until you just live with a scratched up protector, and a perfectly good screen underneath.
While we’re at it… unless you are doing some extreme sports, I recommend a cheap, lightweight case with some key features.
Corner protection: Your phone corners are where it will break when you drop it. Get a case that completely encloses the edges of the corners, and provides good protection there.
Raised bezel: You don’t need to go overboard here, but make sure that your case edges extend past your screen. If you lay your phone screen down on a table, no part of the screen should contact the table.
I used to get OtterBox and ultra duty cases, but lately, I just get a cheap plastic case with a rubber/soft plastic edge for corner protection. No screen protector, and my phone looks brand new. Just avoid getting sand in the same pocket as your phone, or putting two phones in the same pocket.