They usually spray for mosquitos in most counties in Florida. As already mentioned, any 'Off' spray with DEET you spray on yourself. I myself can't remember the last time I got a mosquito bite. I have type A+ blood, mosquitos are more attracted to type O blood.
Palmetto Bugs, are large roaches. Spray the boundaries around your house on the outside and in the garage with ant & roach killer. Especially on the outside of sliding doors, they like to slip in through there. Clean the kitchen well, when you use the toaster, not only clean the tray but take the entire toaster and shake it out over the sink.
The only bugs that bother me are "Love" Bugs. They come every April/May and then return in 120 days, usually Sept/Oct. They are two bugs hooked together, that's why they have their name. They swarm in large masses near highways like 44 and I-75 and anything white, like the trellis at the swimming pools. What makes them so bad is if you have to take trip, let say to Gainesville. You have a black coating of Love Bugs when you return. Don't try and wash them with windshield wipers, it only makes it's worse. You can get a bud deflector (plastic shield), or get netting for grill, or just clean them off after every trip or it will ruin your paint.
I buy this at Lowes for $7 and it works good and it's a good size container with a sprayer. The Wildwood Lowes has over 100 in stock.
