From a Judge perspective, what is necessary to make a Competitive tournament the best it can be?
Darcy, you've already done one thing that escapes many TOs - asking for input, first! :)
I'll add a few things to the already great list others have provided.
I found I usually needed about a ream (500 sheets) of paper for a PTQ - so I'd make sure I had 3 reams with me. Also, if you're thinking of running side drafts, a second event later in the day, etc., then I suggest getting a ream of colored paper; that way, result slips from other events can end up in one Results box without confusing things too much. (That's much easier on the players!)
I don't think this is normal for TOs, but - as a Judge - I felt it was appropriate: I usually provided breakfast (burritos, donuts, something), snacks, water and sport drinks, and lunch - either a cash stipend or something everyone could enjoy. And for those who stay until the bitter end, I'd try to provide dinner, too.
You don't have to have a backup printer - but you do need a plan. My last PTQ had us calling out pairings and collecting verbal results for one round, while my wife ran to Wal-Mart. I've found incredibly cheap printers at places like Big Lots - with those prices, it's probably worth having an extra. (But the extra box didn't always fit in my car!)
That same PTQ, my PA system failed. You may not feel the need for a PA - or maybe the venue will offer one, cheap - but if you don't have one, make sure you have at least one really loud judge on staff. Failing that, you can steal from my friend & frequent Head Judge Luke - who is anything BUT loud - and simply tell the players who are paying attention that you need their help getting everyone else's attention. Word spreads quickly, esp. once the players realize they're not going to get to play until that noisy guy in the back corner shuts up. :)
I never had a retail store, so I would sell vendor tables to local stores/vendors. That helps offset the cost of venue rental. If you can fit your event in a store's play space, they should be overjoyed by the sales opportunities - and free space is a given, in such situations. (At least, that's been my experience - YMMV.)
If you're doing a constructed event, make sure there's someone to sell singles. (Fits into the note above about stores/vendors.) And for either constructed or limited, make sure at least one supplier for new sleeves is still around for the beginning of the Top 8. Be sure the vendor(s) know what the format is, so they can plan; if your format includes Innistrad block, you might try to find a source for blank checklist cards. For Eternal, the vendors probably want “perfect-fit” sleeves for the double-sleeve crowd.
Do you have enough land? Don't leave it in the garage! (Yeah, did that once, too - that same, last, PTQ.) Got tokens? Players often won't, and their solution is lots of little scraps of paper that you get to pick up. :)
From memory, so not at all exhaustive, my TO kit included:
fresh or recently recharged batteries
stapler
lots of tape, for pairings and repairs (most use duct tape, I like Gorilla tape)
paper cutter
scissors (because I'm on my third (!) paper cutter)
razor knife
pens
more pens - and some of a different color for judges
scratch paper (I'd even save scraps from cutting result slips, and cart them to the next event)
tissues and paper towels
hand sanitizer (players really appreciated that)
cash box
receipts (rarely, but a couple players might insist)
deposit slips (so my wife could make a bank run during round one)
PA system
external keyboard w/ numeric keypad (I used a laptop for WER/DCIR)
results box and boxes for land - I bought a six-pack of “plastic shoe storage boxes” from some discount store, they were perfect for 5 land boxes and one results box
power strip and extension cord
That's all I can think of, for now - best of luck to you!
d:^D