J,
I would suggest starting with a Hunter Safety course. Not only do they teach proper firearm manipulation and safety, it enables you to get a hunting permit, and typically (always actually, I believe) the last day is a hands on day which will give you the opportunity to handle a few different types. From there you can make your own choices on which role is most important to you. A few chunks of advice though.
On handguns, I would suggest finding a range that rents by the caliber. I hope they have those in areas other than my own. The set up at a local range here is you go in, get a quick safety briefing, pay a rental fee, purchase range approved 9mm (or any other caliber) and you can shoot any of the 9mm handguns they have in stock, one at a time. As long as you purchase from a reliable company (and the firearm fits your purpose), person fit is the most important aspect of buying a handgun. Glocks may have the most outstanding reliability record to day, but I know a decent group of people who have difficulty with the grip angle, or semi-autos in general. Your gun needs to fit you.
On rifles, in my honest opinion, the best place to start is with a .22 LR. They can be found for very reasonable prices. Bolt, semi, etc, doesn't matter too much. I would recommend a Ruger 10/22, but that doesn't mean you should pass up a nice Marlin or H&R for a lower price. If you decide to compound on the rifle for hunting, 'Curio' style rifles (bolt action Mausers, Mosins, and Endfields) can be found for around a hundred dollars in medium to large game calibers. A mid length lever gun in 30-30 or .308 could fill a hunting/personal protection role. The .308 is a solid caliber for just about any application. Back to starting out, the .22LR will provide you inexpensive and easy beginning phases to the learning process, and building your foundation.
Shotguns, plain and simple... Remington 870. It is not often I strongly suggest a single solution, but in this category the 870 is just simply the best. There are two approaches to owning a shotgun that can fill all roles. One is to buy a shotgun with the shortest barrel legal to hunt with (22" if I recall correctly). 22" is not overly awkward in a self defense role in my experiences (I currently own a Winchester 1200 with a 22" bbl), but if it is for you, a guy can always put a youth-size or reduces length of pull stock on. The other approach is to purchase two different sets of hardware for your 870 receiver. My brother bought an 870 with wood furniture and a 26" bbl at a show (at a screaming price) and then obtained a synthetic youth stock, hogue foregrip, and an 18" bbl (all at used prices) for tactical style shooting.
And lastly, since you asked, for general purpose firearm ownership, I would recommend a shotgun, pump action. Most adaptable to the most applications. As always, your mileage may vary. Good luck and safe shooting.
