I have a 20g saltwater tank, and it really wasn't as hard as some people make it out to be.
First off, live rock... lots of it. This is gonna be EXPENSIVE!!! Figure for about 30 lbs of good quality porous live rock... at $5-9 per pound. Now remove your jaw from the floor and continue onward.
For lighting, I used a Current-USA Satellite Power Compact rig. It's 1 PC bulb... 65 watts... and it's 50/50 Daylight and Actinic 460nm. It's a good spectrum for everything, and enough light for most soft corals. Keep in mind, a 20g long (I'm assuming you're doing a long and not a high tank) is only 12" deep. That light is gonna easily penetrate down to the bottom. Something similar would work.
Next is the other filtration. This one is pretty much up to you. You don't really need to use sponges and filter floss on these as their main purpose is really chemical filtration.... a place to put carbon, phosphate removers, etc. Lots of people on another site recommend an AquaClear 500 modded with a baffle in it to have a small refugium area for sand, live rock, or mineral mud.
For the substrate, don't use silica based play sand. Go get a bag of Aragonite based reef sand. There's lots of styles to choose from, big grain, little grain, pink, white, black & white, live sand, not live sand, etc. When you're buying this though, think about what you want to keep in the tank, fish-wise. If you're gonna keep gobies, blennies, jawfish, or anything else that tries to build a burrow... go with the larger grain sand so they can actually build a structure that doesn't collapse.
Heater.... 50 watts should suffice for a 20g tank. Something like an EboJager or Visitherm.... don't get a cheap heater.
And last, you're gonna want powerheads. Water movement is EXTREMELY important in a saltwater tank. If you don't have good flow, you're gonna get patches of cyanobacteria and other unsightly gunk. The standard answer is 10x your aquarium's capacity per hour.... so 200gph flow for a 20g tank. I'd recommend getting more than one powerhead so you can make sure you don't get any dead spots, or to keep the water from sitting stagnant if something were to happen to the other powerhead.
This is about the cheapest and easiest way to get into a SW tank. Keep in mind that without all the fancy gadgets like skimmers and sumps and such, it's gonna be more work. But, the more stuff you have on a tank, the more things there are to break. And for a small tank like a 20g, a skimmer would probably do more harm than good, removing beneficial nutrients from the water as much as it removes the dissolved organic compounds. Welcome to the hobby, and be prepared for a LOT of learning over the next few months as you get into SW aquariums
Oh, almost forgot... one of the most important lessons I learned from doing mine. DO NOT USE TAPWATER IN A SALTWATER AQUARIUM!!!!!!!!!!! Always use Reverse Osmosis filtered water. You can usually buy it from your local fish store, if you don't buy an RO rig for yourself. Tapwater brings phosphates, and algae LOVES phosphates. Do yourself a favor and stop it before it can start. That's not to say you won't have algae, but you can cut down on a lot of it.
