For a twenty gallon tank, you can do a reef tank on a budget.
Since you want to keep corals, your biggest expense (IMO) will be your lighting. But, you can do lighting fairly cheap using some of the budget brands of LED lighting such and Viparspectra, Nicrew, PopBloom, SmatFarm, Phlizon, Lominie, etc. All of those are available on Amazon. I would recommend that you research what type of corals you want to keep and then pick your lighting based on that...we'll help guide you
Do you plan to have a sump and/or refugium for your tank? If so, you can pick up kits on eBay to build your own sump/refugium from sellers such as jax.racks.123 and Marine Biosystems...just search eBay for, "aquarium sump kit." Then you simply need a cheap tank to silicone the pieces in to create and inexpensive sump/refugium. Of course, you'll need to either drill your tank for an overflow or use a hang-on type overflow.
You'll also want live rock of some sort. Many people build their tanks on a budget using just dry rock. Some use only live rock and others (like my current tank) use a combination of dry and live rock. You can get really nice live rock from places like Tampa Bay Saltwater, KP Aquatics, Gulf Live Rock and Salty Bottom Reef Company.
You'll also need to decide if you want to use a protein skimmer or not. I personally use a skimmer but, many have very successful reef tanks without one. This will be another significant expense. If you have a sump/refugium, you can use an internal skimmer. If you choose not to use a sump/refugium, you could add a Hang-On Back (HOB) skimmer.
That's just scratching the surface a bit but, gives you a few things to think about. As always, feel free to post your questions and we'll be happy to help provide guidance based on our experience.
A couple things to remember in this hobby.
1. Take your time...nothing good happens fast in this hobby.
2. There is no single right way to set up and maintain a reef tank. There are many options and what works for one person may not work for another.