For $45, you're asking for a lot of performance... and in an odd size. 205/50 is going to be the typical performance profile in that size range. 205/60 is going to mostly be all-season tires.

I'd suggest you go to the Tire Rack and search for tires in your size, and then narrow your search to the best high-speed-rated tires you can find. (you don't really need the rating for speed, but higher rated tires generally have stiffer sidewalls, which are better for handling) Look at the Tire Rack's reviews, customer reviews, and customer average ratings. They aren't gospel, but they can certainly show the overall trend for a tire. (ie: If it's crap, everyone's going to say it's crap)

I just ran a quick search for that size, and I've actually tried several of them. They're not the top-end "ultra high performance" summer tires, but some of them aren't bad. Quick synopsis of my 205/60-15 experiences, FWIW:

Yokohama AVS db (not the new S2) - These are presently on my wife's car. Excellent all-purpose tire. Good grip, reasonably sharp response. Their AVS heritage is apparent. They ARE quiet as their name implies. They didn't start making noise until I let one of the rears get out of balance... and then moved it to the front. Great all-around tire. For FL, probably better then the SP5000.

Pirelli P6000 - Formerly on my wife's car. I was pretty happy with them. Sidewalls were soft for a Pirelli, grip was decent. My only gripe with them was that all of the tiny grooves in them picked up itty bitty pieces of gravel and held them forever... making them noisy, and probably also affecting grip.

The new Kumho's might be okay. I had a set of 712's and wasn't impressed with them. YMMV.

Now, if you can get your sidewall down to even a 55 (205/55-15), your options open up considerably. You won't get anything great for $45, but you can get:

Dunlop SP5000 Asymmetrical - Bought these for my Miata to get me through my last winter in Kansas. They had good "light snow" reviews, and good wet and dry weather reviews. I was impressed with their grip! They even autocrossed well. But the sidewalls were soft, and responsiveness was weak as a result. Sold them as soon as winter was over, and bought a set of 205/50 Azenis!

Bridgestone Potenza S-03 - These are on my Miata right now in a 195/50. They rock! A step down from the Azenis in grip, and maybe stiffness, but better in every other way. (wet traction throughout the range of tread depth, tread life, noise, etc) If I don't cheap out, I'll probably get another set.

Did any of that help?