If you are serious about seahorses, you will need to do quite a bit of research. Providing you with all the info needed cannot be accomplished in a single response post (or even a long thread).
I'll try to help you get started though ...
First, read every day. Read back through the many seahorse posts on this forum. There are other seahorse specific sites and books dedicated to seahorse husbandry. Read as much as you can and you will start to see what's involved. It will all start to come together. You will also see what has worked and not worked for others. This alone will answer many questions. I'm not trying to discourage you from asking questions, but questions asking for clarification or specific opinion are much easier to answer in a response.
To respond more directly, a 20 gallon long makes for a very poor sh tank, as it simply does not have the height most species require. The only available seahorses I know that would work in that tank, are cold water species ... requiring a chiller.
You will find many differing opinions on the best filtration/setup, each with good reason behind their opinion. As you read, determine for yourself what makes sense and what seems to work best for others.
When you do buy seahorses, choose a professional breeder (there are a couple that frequent this site) and choose seahorses that have been bred in an aquaculture settings. I consider from where you get your horses, THE most important decision you will make as a seahorse keeper.
Learning about seahorses is fun in itself and you will likely be amazed at how passionate seahorse keepers get about their hobby.
Hope this somehow helps. Good luck ... and come back with more questions as you learn.