Well, they require at least 18 inches of vertical height. The easiest are definitely the erectus, they are the most common and probably the hardiest. They dont really need to be a tank all by themselves, they just need to be with tank mates that wont compete for food, eat them or bother them (so no open swimming, crazy fish like angels, tanks etc).
They also need lots of things to hitch onto with their tails because they arent very good swimmers. People say that they dont like a lot of flow because they dont swim well, but i find that they really like the faster flow as long as they have something to hang onto.
Also it is SUPER important that you buy captive breed seahorses, not wild caught or tanked raised. The last two are usually very problematic, they arent adjusted to frozen food or tank life. They usually arent very hardy and most often die.
If you are thinking of seahorses please do your research first, they do take some special care. A great place to buy from and ask questions is seahorsesource.com. The owners/breeders are really great, nice knowledgeable people. seahorse.org is another great place to check out. However, hands down the best way to learn about seahorses is to take the FREE seahorse lessons from Pete Giwonja at seahorse.com (you just email him and ask him to send you the lessons. There are 10 and he will answer any questions you have after reading through it. He will also answer any other questions and help you plan your tank. )
Im sure im forgetting lots, but that will give you a start!