Well the first question is what type of seahorse do you have SeaStallion, mine are Erectus, which are probably the easiest to breed and raise. Some such as Reidi are pelagic and require a totally different setup from Erectus that have benthic fry that can hitch from birth.
Having said that my setup is relatively simple. I have a 20G tank with a 10G sump. I have the smallest overflow box I could find on the back of the 20G. I then bought two of the plastic tank dividers. One I used to divide the tank into about half. The other I cut up and glued over the water slots on the overflow box, because as tiny as they are, little seahorses would get sucked right in, but the divider has small enough space to prevent that more or less. I them got some plastic decor for the seahorses to grab onto, ones with thin bits are best since they have tiny tails.
For the sump I got a HOB filter rated up to 30G, a heater, a small skimmer(not getting a lot out of it yet though still working with it and honestly I think it's overkill), a bag of carbon, and the smallest Maxijet pump for water circulation I could find. I want to say it's like the 300 model or something, it basically circulates a very small amount of water after having to pump up about 3-4 feet.
I put the baby seahorses in the side of the 20G that does not have the overflow box on it, even with that tiny flow they still get stuck to the overflow box if they get near it and their little tails can get pulled in but not their bodies, making it a pain to get them out again.I reserve the side with the overflow box for my older seahorses, I'm finding that even at a month old I still don't let them on that side, thinking 1.5-2 months might be the magic number or basically when they get ready to eat adult brine shrimp.
For feeding I keep 4 cut off soda bottles of brine shrimp and a bucket of rotifers going. Now not sure if the rotifers really do anything but I feed them in addition to the bring shrimp for the first two weeks. For the babies for the first two weeks they basically get day old or less brine shrimp. The BBS can't eat yet so I don't enrich. I only try and feed what can be eaten in a couple of hours, I usually see some food floating around but if a collection of BBS form near the surface after that I know I fed to much. My big guy get a bunch of live adult brine shrimp, I'm trying to work on getting him over to frozen without much luck so far. After the babies get a couple weeks old I start letting the BBS get a couple days old so that I can enrich. Now I do it two ways. Once a day I'll put them in a small container with Selcon for about an hour or two before feeding, I keep all the brine shrimp alive with green water though, so even when I don't use selcon they are still full of green water, which I think adds a decent bit of nutrients to them. I would like to use selcon for every meal but honestly the whole process is already to time consuming, as much as I want them to survive I have to live my life and still take care of my 90G DT, 10G freshwater, 2 cats, and dog. (Yes my house is a zoo)
I feed three times a day, the professionals feed 5 but my daily schedule just does not allow that. They also suck out the excess food and seahorse poop after every meal, again I don't have the time or capacity to make that much saltwater so I just do it once a day, normally about an hour or two after their afternoon feeding if I can. I'll suck out everything I can off the bottom and end up changing about 3-4 gallons or about 10% of the water daily. If I think the tank is maybe a bit gunkier than normal I'll do a larger water change until I am happy. But I've found with a 10% daily change the water quality stays fine.
So that is what I do. My first setup was a 10G with a divider and a HOB filter and bag of carbon in the half without seahorses, that worked well too. I only upgraded because of the massive amounts of babies I keep getting stuck with and because that tank was sitting on the dining room table, so I made a more permanent setup. I figured even if my seahorses stop having babies I can use it for a quarantine/hospital setup.