I am always on the lookout for the right tool to help how I run my sessions, so I appreciate threads like this.
That being said, in practice, I don't use much:
Official DM screen, but I never look at the charts, tables, etc, during play, even when I should. I usually forget what's on the damn thing. In practice, I find it is good at hiding my notes and rare secret rolls from the players, but I try to keep my eyes on the table and the other players. I did recently purchase a customizable screen for a Cthulhu game I'm running. I put a one-sheet summary of the adventure (so many more characters, dates and "clues" to keep track of) in that, which was helpful, though incomplete because I ran out of time sketching everything down before the session started.
I keep a notecard or a sticky behind the screen with every PC's name and their passive perception. Sometimes I'll ask for languages. In Cthulhu I keep a note for every Knowledge skill they have.
We've stopped using mats because cleaning them off was too much of a pain. I just use a piece of graph paper or printer paper these days. Some of the players are willing to map themselves, which is a huge help (frees me up from having to lean over the screen drawing corridors all the time.) I've thought about giving a dry erase board a try, just to allow for drawing larger maps that are easier to see. We haven't run gridded combat in a while, but we often throw bottle caps, coins and under-utilized d12s on the table to help keep track of larger combats. We gave up using actual minis, as we travel by subway to our game every night, so packing them around was a pain. I've thought about printing numbered chits on card stock to use in larger combats, so I can more easily remember hit points for larger groups of monsters.