You really don't need a lot of elaborate equipment.
Tank: Think tall, rather than long. Also consider 25-30 gallons for a pair of the more common species (e.g., erectus, reidi). Increase that by 10-15 gallons for each additional pair.
Light: Seahorses only need enough light to see. Normal flouresent lights would work. I like a bit more, so I can see them better.
Filtration: Good water quality. Some use sumps, skimmers, refugiums, live rock, etc to keep water quality high. Some use a simple hang on mechanical filter and do frequent water changes. If you are dilegent with tank maintenace, you can get by with less.
Air: Seahorses require higher oxygen levels than most fish. Make sure there is some turbulence at the waters surface. I also recommend at least one airline. I also use a battery operated air pump that starts up when the electricity goes out, as a backup. Yes, its that critical, imo.
Substrate: Seahorses really don't care. It can be bare bottomed to a deep sand bed.
Plants: Unless you are already familiar with saltwater plants, I suggest you concentrate on learning and tending to the horses needs first. Trying to tackle the two at the same time could get tricky.
Hitches: Seahorses need rest areas where they can sit still, usually anchored by wrapping their tail around something. Real or fake plants, corals, rocks, etc would be enough.
Temp control: There are cold water species. If you get these, you will definetly need a chiller. Even the tropical species need cooler temps to reduce risk of bacterial issues. For erectus and reidi, shoot for 73-74F range. Depending on your lights, equipment, house temperature, etc., you may or may not need artificial cooling. Simple economical clip-on fans can drop the water temp a few degrees. That may be enough. Just make sure you can keep the temps consistently in the low/mid 70s.
HTH