No fingerprints means a less glossy protector (but whether the fingerprints show or not, they're there, and will eventually smear across the screen protector, making the screen look dull.). About all you really want from the protector is that when it gets scratched, it's cheap and easy to replace. (It's going to get scratched - even tempered glass will.)
If you're not going to put the phone into an Otterbox Commuter or Defender (which is what I recommend - I wouldn't drive over a phone in one, but it sure feels as if it could take it), any 3/$5 plastic protector is good. Three of them should last at least as long as you want to keep the phone (my first one on my Note 3 lasted about 15 months, until I peeled it off because the phone was already in an Otterbox - and it didn't have a scratch on it - my wife's is still on hers after 22 months and still looks new, and I still have a 3rd one in the package).
For fingerprints, get a microfiber lens cleaning cloth and a little spray bottle of lens cleaning solution (any eyeglass place, including the ones at Walmart, carry them). Spray a corner of the cloth, clean off the fingerprints and use the dry part of the cloth to dry the screen.