I can't believe no one has mentioned this before, but several ranges have rental guns. You will probably have to buy 'their' ammo, but it will give you a chance to shoot several guns and get a feel for what you like best.
For a first handgun I would recommend a single-action revolver over a semi-automatic pistol, preferably a .22 caliber (Long Rifle .22, not a high-caliber like a .223 round). Shooting single-action (cocking the hammer, then pulling the trigger) for each shot will help you to focus on your form instead of just throwing a bunch of lead at the far end of the range. Shooting a .22 has the triple advantage of low recoil, low report, and low price. Once you get comfortable shooting the .22 you can move up to a .38 double-action revolver or a 9MM semi-auto. While it's not as cheap as a .22, you'll then learn to deal with recoil and you have the advantage of using this as a defensive weapon (home defense, concealed carry, etc.). While you could use a .22 for this in a pinch, it's really not practical.
Once you feel you've mastered a .38 or 9MM, then you can move up to one of the heavy calibers like .45 ACP. But I wouldn't recommend jumping out there and starting out this way without working up from the smaller calibers. You can do it, but you're going to have to overcome your initial instinct to flinch every time you pull the trigger.
Whether you choose to make this move with 'rented' guns, or buying a couple yourself, I strongly urge you to start with a .22 before getting anything bigger. Otherwise, you're likely not going to enjoy it very much and will likely become discouraged by the result of your experience at the range.