Hardiness is "in the eyes of the beholder" kind of thing. IME, one species is about the same as the others in MOST respects but I DID find H. comes to be problematic but that was about 15 yrs ago and I certainly didn't have the knowledge I have now. If I wasn't at my age I'd like to have given it a try again though.
H. abdominalis is far and away the one that gives the least trouble and IMO, it's because the bacterial problems are SO MUCH reduced due to their need to be kept at 68°F or lower. If you can meet the temp need then the rest is much easier.
However, as they are all about the same when it comes to keeping tropicals, there IS a difference in breeding as ones that produce pelagic fry like reidi are more difficult than the ones the produce benthic fry like erectus.
As already mentioned, species you buy is really limited to what is available at the time and that is predominately erectus for North America if you want quality captive bred seahorses.
Often LFSs get in offshore imports of different species but that is another problem in itself that I don't wish on ANY newcomer to the hobby.
As for learning about the hobby before actually getting in to it, you can add another source to the already mentioned ones and that is to join Dan Underwood's "Seahorse Source Group" on Facebook. When you are on the group page look for the "FILES" link and click on that for links to a LOT of great information Dan has put together.