Despite my discussions with Ken about the finer details of differences between sword methods, Ryu, approaches, etc, in this regard, from the standpoint of someone with no experience, they really are all the same (just to make you happy, Ken!). The benefits of each are pretty much the same, but certain approaches may appeal more than others. For instance, I train in two Kenjutsu systems and an Iai system (all Koryu), as well as other systems that have Kenjutsu in them. I have also been given the opportunity to visit other systems, and the ones that I train in were chosen because they are the ones who's approach really appeal to me and my personality, I deliberately and consciously didn't accept training in others. So the best bet is to visit as many options as are around you, and see what "calls" to you. You may be surprised to find that what appeals most is Iaido... or Kendo. Or Jodo (as you learn sword as the attacker).
It may be a modern (Seitei, or Atarashii [for Naginata]), or old (Koryu), but if you are looking at Koryu, then be prepared properly for it. And the first step to understanding what Koryu is all about is reading the following article from Dave Lowry:
http://shutokukan.org/join_the_ryu.html Read it a number of times before you decide that this is something you're interested in.
Now that you've read that, here's the good news.
You haven't said where you are, exactly, but St Petersburg and Tampa, Florida, have been mentioned, so my guess is that you're not too removed from there. And Tampa Bay seems to have a dojo of Yagyu Shinkage Ryu Heiho (Kenjutsu) one of the two official Ryu-ha of the Tokugawa Shogunate. This is one of the most famous and respected sword schools you can find, and if you have to travel an hour or two to get there, all I can say is that that is a short trip compared to many who train in such things. Their listing is found here:
http://www.yagyu-ryu.org/tampa.shtml, and frankly, you will be hard pressed to find a more reputable system, particularly around your area. This is a system people travel across the world to train in, so you know.
PS This is one of the systems that Dave Lowry, author of the above article, teaches, as does Meik Skoss, a highly respected individual in Koryu circles. Just so you know....