I use a screen. I did use it standing and hide all my minis behind it so the players couldn't see what I was about to pull out. I'd also roll behind it.
But I had one player that the other players told me was lying about his rolls. He sat right across from me, so the screen blocked my view of his rolls. He would get upset if anyone else sat in "his" seat, even though he had kind of hijacked it from another player initially. So I just started putting the screen flat.
I wanted the information on the screen (which I do occasionally reference) so now I play with the screen laying flat and the minis on top of it. I pull out so many minis each session that even with my players able to see them, they still don't know what's coming next. I still keep the minis representing unique NPCs/monsters out of view still until time to put them in the fight.