What part of SW FL are you in ( I know FT. Myers very well)?? I lived in Fl and grew roses in Southeast and Central Fl. for 40+ years. Growing roses in 24" pots is very doable. Over those years I grew every kind of rose in pots except climbers. A lot of own root roses do very well in pots. The trick is in the soil and watering. You will need a light weigh potting soil to start off with. There are a lot of roses out there that are pretty disease resistant. Do a little research before buying. Having roses on the lanai, you will probably want something that has a great scent. Don't be intimidated by Florida. You can have roses 11 month's a year.

Not too far from Ft. Myers - Ave Maria. ☺

I'm not in Florida, but I ordered some roses this year from two nurseries down there -- Rose Petals Nursery and Angel Gardens. Their roses are own-root, and they both have nice selections of a wide variety of types. If you're not bent on modern roses, I think you'll do very well with Chinas -- they'll bloom pretty much year-round for you down there. Teas and Noisettes are probably too big for pots. Many Polyanthas will also work. As far as other types, perhaps contact the nurseries I mentioned and ask what they think. They're not that far South, but they'd have a better idea than I do.

:-)

~Christopher

The key is sharp draining soil. My biggest problem with growing roses in pots is root rot. I've lost many roses to it. They start to die back and then you can see the stem getting black from the bottom up.
I started to look closely at what kind of soil they came in from the nursery and I noticed it was very barky and not very dense at all. So I tried to mimic that. Now I just buy a special soil that comes for bougainvilleas and its been the perfect fix.
I get it from home depot and it looks like this:

I still sometimes loose roses, but not nearly as many and the ones I've lost have not been in this special soil. The heat works against you because in pots the soil will get very warm (with the sun beating down on it) even warmer than the ground. Combine that with too much moisture and its a double threat for root rot.
The down side to this is you'll need to fertilize often because this barky, loose soil wont hold nutrient as much.

Here is a list of roses that have done well for me (Ft. Lauderdale area, zone 10)

Belinda's Dream-pink, modern pointed form, fragrant (this is an excellent starter rose that is very forgiving. If you get one rose in South Fl it should be this one).
Easy Does it-orange/pink blend
Cecille Brunner-many tiny pink blossoms about the size of your thumbnail
Quietness-pink, old fashioned, fragrant
Duchess De Brabant-medium pink, open loose blooms, fragrant, easy to grow
Don Juan-(not suitable for pots but an excellent climbing rose, the best for the area, large red fragrant blooms)
Tamora-(apricot colored David Austin rose, old rose form)
Darcy Bussell (also a D.A. rose with old fashioned bloom form, deep red)
Miss All American Beauty-hot pink (magenta) a very tough little rose
Fragrant Cloud- red orange, very fragrant, very large blooms, excellent rose
Fragrant Delight- somewhat sloppy form but very large fragrant blooms
Love-very floriferous light red blooms with white reverse on the petals, somewhat sloppy form but always blooming
Ingrid Bergman-(red) very fragrant nice disease resistance
Dick Clark-very floriferous, beautiful deep pink/yellow blend
Julia Child- yellow blooms, great rose, blooms a ton, good for a pot
Secret-pink and yellow blend, good for pots
Bride's Dream- good for a very large pot. very pale pink and excellent form. A very elegant rose

A few things to keep in mind. When it comes to containers always go taller as opposed to wider. If you put a little mulch on top it will help keep the soil cool and retain moisture but should not cause root rot (especially if you use the soil I recommend). Lighter colored containers are better at keeping the roots cool. Don't get black as this will make it worse. Terracotta pots are controversial. Some say they wick moisture away from the roots keeping them cool. Others say they act like an oven and "bake" the soil. You'll have to try them at your own risk but I think if you keep them well watered, they are a good way to keep the roots from rotting as they 'breath'. Assuming of course its not glazed terracotta.
Plastic pots work well in any case.

If you decided to put the roses in the ground you'll want to get them grafted on fortuniana, but otherwise you can grow pretty much any rose you like in a pot.

Chamblee rose nursery online is a good source as well as the two mentioned in the posts above (angle and rose petals).

Good luck and post photos once you get them going :)

PS
Pruning is done either in January, or at the end of the summer (or both if you want to keep them small). I find mine are usually at their peak in Jan so I prune them in the fall after the summer has them all tall and gangly. You don't have to prune them too hard (or at all even) unless they are grafted on Dr. Huey in which case you'll want to give them a nice hard pruning at least once a year. If you don't they will die in 2-3 years because of lack of rest (no winter rest here), but pruning them hard lets them have that rest and will increase the life span. I usually prune mine when they look like they need it (getting tall and leggy) and not by the calender.