It's Summer. A great time to go there (as compared to Fall/Winter rates).
A condo that could go for $3,000, 4,000 or even $6,000/week in Winter may be renting for $1200 to 2400/week in July.
How old are you and do you want quiet or do you want to be near the Village?
Older and quieter - I would tend towards old properties like the Jamaica Royale or Aloha Kai south of the Public Beach - these should be about the cheapest stuff you can find "on the beach".
Younger and quiet - I would go for one of the newer towers like El Presidente, Excelsior, Midnight Cove - you'll pay for the high rise though!
I'm not too familiar with the stuff North of the public beach, but these properties will get you nearer to downtown village with shops, restaurants, bars, etc.
Remember the entire Siesta Beach area is about 3.5 miles long, so in my mind everything is walkable.
I'd call a real estate office on the Key and try to see what they have listed if you need reservations. If the Beach is too expensive, go for Bayside stuff - may be cheaper - although the boaters like those properties, too. If you stay in Sarasota and decide to drive to the beach, stay "west of the trail" - a reference to the Tamiami Trail (Rt. 41) that runs North-South. If you go east, the world gets rougher and hotter as you lose the gulf breeze.
PS, it has got to be the nicest beach in the world to walk. I own property there but its not for rent. A nice quiet place and those of us that own would like it to stay that way.