Di = Dionized water. you can buy it cheap at CB pets if you don't have a filter, it's actually taking stuff out of the water (almost everything) not putting stuff in, so no additived. CB pets has an awesome commercial grade DI system that will make the best water you can absolutely get.
As for the other stuff: I have had some bad experiences (great for learning!) that will hopefully guide you.
1) 20 is small, heat WILL be an issue. be careful how many power heads you add to the tank, this includes filters, skimmers, etc.. anything that has a moving part will add heat. (then add light heat and your actual heater.) I stewed my 30 gallon by putting in to many pumps, I was pushing the upper limit on heat, then one went bad and presto. coral stew.
Even though people knock them, I like the powersweep powerheads, they are a cheap ecenomical source of flow in your tank, but you have to be 'religious' in your maintenance of them, luckily, this is easy enough thanks to a lesson from richard. buy a 5 dollar bottle of muratic acid from home depot and dunk your powersweeps (take them apart first and wear gloves!) in a weak solution, and watch your powerheads make like an alka-seltzer tablet. I cleaned one 4 weeks ago that I thought was a lost cause, works like a champ now, looks like it was fresh out of the box! I would think that a better solution than putting in lots of power heads, or bigger ones, for more flow.
2) don't skimp on a skimmer. as was said, you can get away without having one if your dilligent in your tank maintenance. But I would say there is good argument that a cheap skimmer is not better than no skimmer, for instance, I had a prizm overflow it's collection cup once because they are darn near friggin IMPOSSIBLE to dial in... (at least for me) and the mess, well, it was smelly... People who buy cheap skimmers almost always end up buying better skimmers later.
I don't know anyone who has experience with the coralvue octopus skimmer, so I can't comment on that.
However, I do have experience with a Remora that makes stinky nasty skimate!
And it just so happens, that AquaC is FINALLY releasing their NANO Remora this year, designed for tanks in your size range, and undoubtedly cheaper than what they have out now. That would be my buy if I was doing a tank that small again.
"Maybe in order to understand mankind, we have to look at the word itself: "Mankind". Basically, it's made up of two separate words - "mank" and "ind". What do these words mean ? It's a mystery, and that's why so is mankind." ~ Jack Handey