Very good questions and welcome to the reefing community. There are plenty of good people here to help you go the right direction. I've been reefkeeping for 6years and i have 2 reef tanks going now (both listed in my signature).
Lighting is a very important thing for the corals. It affects the growth rate, pattern, coloration and density of the coral. To get a good breakdown of the lighting read Coral Lighting and Acclimation
. It'll give you some insight into what you will be expecting. You will need to give more information on where you plan to go. Yes, you will need to get rid of the spotted puffer because he will chew on some things.
As for a skimmer... this is a personal preference, IMHO. You can use a skimmer for a tank this size, but it's not mandated. If you keep up with the weekly maintenance of the tank and do 10% water changes a week or 20-25% changes every 2wks or so, then you'll be fine without one (this is assuming you don't overfeed, and over stock your tank with fish). If you must have a skimmer in the tank then i would recommend a AquaC skimmer Remora. They are efficient and do a great job of keeping bubbles from the tank as well as silent. Others will say SeaClone or Prism, or Skilter skimmers, but they are no where near as good as the AquaC and it's not that much more expensive.
LR and sand are very important to a tank with no mechanical filtration. The Sand will denitrifly the tank and create a home for critters that will eat the negatives in the tank and the LR does the same thing. Corals love to grow on LR and success without the LR is, though possible, very poor. in the eventual, you will find yourself getting LR anyways.
You will need some lateral flow as well. So you'll need a powerhead and especially with corals. What are you going with? Soft corals? LPS or SPS? very important things to look at. Soft corals like flow but not as much as LPS and SPS require a lot more flow then most other corals. Where do you plan to go with this tank? A MaxiJet 1200 or 2 will give you all the flow you'll need for a 20g high. The general rule of thumb is 10xgallons. So if you have a 20gallon tank then 200gph is fine, if you are going to get LPS and SPS then you'll want to follow the 20xgallons rule which will be 400gph. They are in expensive and with smaller pumps you can change the patter easier then one large pump.