We definitely need to know more about what you're looking for in terms of level of care, just HOW big, etc, before we can make recommendations.
As Fuzzyviper stated, Sulcata tortoises are the largest tortoise species commonly available for sale, and the 3rd largest in the world (the others are Aldabra and Galapagos, both much more expensive and harder to get/find in the states, as well as MUCH larger). Large males can exceed 150 lbs full grown, and you're looking at a tortoise that's 3 feet in shell length. That's a BIG tortoise! They need a great deal of land... A half acre would be a great size to start. You would need to invest in a big heated "sleeping box" for cold weather (i.e. anything under 70ish), since at a certain point they're simply too large for an indoor enclosure unless you go all-out converting a large basement or the like. They eat a LOT, and often times just grazing on the yard isn't enough because they have a habit of eating all the grass down to dirt! They will wreck your yard, dig burrows that can become a big problem if it hits a water line or anything of the like, and are quite good at knocking over walls or finding somewhere to climb and escape so they can go explore the neighborhood. They are VERY outgoing, though, and can be a great addition to the family
if you're PREPARED for what's involved!! If you do a search on
TortoiseForum.org for "Bob" posts by maggie3fan, you can see some of the "great" adventures that come with owning a giant Sulcata!
One other benefit of Sulcatas--you have plenty of options, whether you want to grow one from a hatchling (plenty of breeders around), or even if you want to get one that's already good-sized--there are often large Sulcatas being sold on Craigslist and the like, as people realize what exactly they got themselves into and decide to offload the growing tortoise they've realized they can't accommodate.
For slightly smaller tortoises, you have Leopard tortoises. These guys aren't as obtrusive or destructive, don't burrow much, and are generally much more shy and "delicate," so to speak. The babcocki leopards (the more common of the two subspecies) stay much smaller than Sulcatas--AFAIK, they don't normally get bigger than 40 lbs. The pardalis subspecies, which is much less common, gets much larger (not 100% sure on adult size--much closer to Sulcatas, but I believe still not as big) and tend to be much more outgoing, personality-wise. Leopards are beautiful tortoises, and, personally, one of my favorites! This is my little one... He's still just a baby at 115 grams, and growing like a weed:
Yes, I keep him on a moist substrate and his shell is WET in this picture. I do not believe in the "old" way of keeping hatchling Leopards OR Sulcatas dry and restricting water. Restricting water and keeping them in a "jerky maker" (so to speak) set up only leads to dehydration and an unhealthy tortoises. Too many Sulcata and Leopard hatchlings wind up dying of renal failure due to this, and those that survive go on to present with extremely prominent pyramiding of the shell. I'll refrain from going on a tangent here, but I will recommend that you browse around the forum I linked above (Tortoise Forum) for more information on Sulcata or Leopard care. You can find a better explanation of "wet" vs "dry" keeping, pros/cons of both, etc, etc, as well as much more appropriate methods of raising a hatchling than tossing it on alfalfa pellets under a hot light with no water.
And on that same note, Sulcatas and Leopard tortoises both (the "desert" species, that is) actually THRIVE in the humid climates. Sulcatas actually seem to thrive best here in the states when kept outdoors in Florida--the closest thing the continental US has to a consistently hot and humid climate.
Okay, now that I'm done with that tangent, LOL, back to the original topic...
Other "big" species... Redfoots aren't really "big," but not "small" either. You're looking at about 10-12" max, if I remember right, with these guys, depending on what locality you get (i.e. Cherryheads stay much smaller--more like 8" max, I believe). Still small enough to house indoors during the cold weather, but also a pretty good size and would thrive in your warm, humid climate. They're outgoing, and have slightly unique care needs--while most other tortoises should only be fed fruit rarely or never and don't eat any animal protein, Redfoots need both fruit and animal protein on a regular basis. They are definitely very beautiful, and very interesting to watch. They are pretty commonly available captive bred, too.
Yellowfoots are another one. More secretive and somewhat larger than their close relative, the Redfoot. Almost identical care requirements to Redfoots, just in a bigger (somewhat less vibrantly colored) package.
There are various other tortoise species, depending on how big is "big," how much effort you want to put into care, whether you want any indoor time or outdoor only, and overall just what appeals to you. I would recommend
TortoiseForum.org for learning more about any of these. There's some good care sheets around for all of them, too, I just can't remember any off the top of my head. Lol
As far as turtles, there are a great many species that get huge, but the big species are, as a general rule, aquatic. If you want a big pond with giant turtles, though, there's plenty of options... For example, female Red Ear Sliders can reach 12" as adults. Softshell turtles get huge. Cooters and most (if not all) the other Sliders get very large, too.
http://austinsturtlepage.com/ is a great resource for Aquatic turtle species, plus there is a forum where you can ask for more specialized and specific advice on what species of turtle is right for you.
Beyond that, I'm not going to be much help--I'm not much of an aquatics person, so the only aquatic turtle species I know much of anything about are RES. =P
Good luck with your decision!!