I would stay in the four to five inch range. This means a standard sidearm-sized handgun, which will be more pleasurable to shoot at the range, and will be slightly more accurate due to the longer sightline length.
There are a number of pistols that fit your requirement. Look at the standard-sized Glock 17, Springfield XD, S&W M&P, FN FN9, Ruger SR9, CZ 75 or 85, and a polymer Sig whose model number I can't remember. These are fairly close in price to each other. Slightly higher on the price scale are the H&K's, Sigs, and my personal favorite for range use, the Walther P99.
If you have small hands, then look at the compact versions of the Glock (model 19), XD, M&P, and P99. Any smaller than that and you are now looking at versions that are more useful as a concealed carry, and less of a range gun. Of course all of these can be used for home defense, but keep in mind that a larger handgun means more bullets, which is something nice to have if you ever have to defend your home.
Good luck on your evdeavor. I should warn you that getting into shooting is a slippery slope. By this time next year, no telling how many handguns you will have....