To my knowledge, you won't find a condo that has its own pool. A condo is in a multi-story, multi-unit building and there's frequently a resort pool. I know Windsor Palms and Windsor Hills have town homes with many having a small splash pool. I've just checked on town home prices for March 2007 and found several in Windsor Palms that would be in your price range. Windsor Hills is newer and seems to be higher priced right now, so I'll be sticking with Windsor Palms.
In general what the prev. poster said is true. Most condo/townhome's don't have their own private pools. Pretty much all of the communities where they are located to have pool's though. Now there are a handful of townhome's that will have splash pools on the lanai (sp?).
Just to name a few. If you rent direct you should probably be able to find something in your budget range, especially since you won't need pool heat in the summer. If you go w/ a management company, your odds are a little less likely to fit into that range w/ tax.
Now, the other thing to consider would be to stay in the Davenport area--- there are many great developments that way like Regal Plams, Hampton Lakes, and Cala Bay Parc. The drive will be 15-20 minutes depending on traffic. The stores and such are a little less hectic in that area. We found the drive to go quickly each day too. The bonus to stay out that way was we found we could get a lot more bang for our buck. The houses were bigger w/ more amenities for similar prices of a smaller bare bones house in places like Formosa Gardens and Emerald Islands. Just another avenue to consider.
As Kilee said, you can get a really nice house out on Hwy.27. Many are in gated communities. Regal Palms (condos and maybe houses too, I can't remember offhand) has a very nice pool area (even has a Lazy River).