Same suggestion here: go to a local pro shop, and ask for e beginner kit. Normally, pro shops have good offers on sets consisting of a ball, shoes and a bag. The ball will be either a polyester ball (good for true beginners and hobby bowlers who just want their own ball) that should be drilled witha conventional grip, just like a house ball, or an entry level reactive for the more ambitious user which can be set up with a fingertip drilling - even though I'd recommend the latter as a second step.
I would not buy from an online pro shop - nothing beats personal contact and counseling, especially when you are new to bowling.
The pro shop owner will either watch you play, if you have some experience, and/or measure your hand for a proper ball setup that matches your hand.
Just as Rileybowler mentions, beware of being talked into a high end ball that does not do anything for your game - better take a simple low end piece, and invest the money into training or a coach.
--------------------
DizzyFugu - Reporting from Germany
Confused by bowling?
Check out BR.com's vault of wisdom: the unofficial FAQ section
Secrets revealed: What's a fugu?