Wow, the $64 question! Amateur Radio has many diverse interests and activities. It's hard to say were to start.
First, I would recommend getting involved with a local radio club. Check with the ARRL web site for information on locations and dates of meetings for one near you. Hopefully, you can find one that is receptive to newcomers. Most are.
Second, subscribe to QST and other monthly periodicals. If your lucky, your library may have them. Mine does.
Here are a couple places to start:http://www.w5yi.org/AmRadio.htmhttp://www.remote.arrl.org/hamradio.htmlhttp://www.arrl.org/FandES/field/club/clubsearch.phtml
Best radio for the beginner? It all depends where your interests are. You might want to wait until you are a little more familiar with HF vs. VHF etc. before making a purchase. Here is where the experience of an “Elmer” or Ham mentor comes to the rescue. Talk to other Hams and get their advice. Beware, some of us are fanatics about this mode or that band and such lunacy is contagious!
Now the easy question. Yes, packet radio is done on Ham radio, mostly on VHF. Packet is not the only digital game in town. On HF, you will find many other digital modes. You will learn about them as you go along.
Hope this helps to get you on your quest. Give me a shout when you get licensed!