I started with a 20g reef tank myself. It isn't a bad plan to go that direction first. I would love to have some seahorses but they are INCREDIBLY hard to keep alive in an aquarium, and they need a very well established tank as well.
How much experience do you have with keeping fish?
If you are going a 20g FOWLR
I would keep at least 2 if not 3 powerheads in a tank. I keep a 10g refugium on top of my 20g tank just to stabilize things a little bit more. Going smaller isn't easier in fish keeping, and it is especially hard on saltwater tanks. I would definitely suggest getting the largest tank you can as it will keep levels from fluctuating quite as much.
A filter isn't necessary as long as you have ample water flow and a good amount of live rock in a tank. For a protein skimmer, I run one on my tank; but since I've had it since I started the tank I couldn't tell you how big of a difference it makes.
For other equipment I would suggest a master saltwater test kit, refractometer / hydrometer, and a small heater and air pump / powerhead to mix your salt.