Buying bowling equipment is a major investment so I suggest you think it over before seriously considering it. It's not as simple as having a ball and shoes unless you want it to be a once or twice a month thing. Pretty soon you'll need a bag to put everything in it. You'll need to purchase a wrist brace unless you have strong wrists. Bowling ball cleaners to maintain the balls surface unless you can afford to replace it every couple of months. The accessories are endless just like flashlights. The better you become, the more you'll want/need. But IMO, by far the biggest expense you'll have is bowling lane fees. Once you get hooked, you'll probably be doing it 2 to 3 times a weeks at a minimum playing four games at least each time.
You definitely will need your own ball because you need to have it drilled to your hand size & specs. The logic here is to put as little strain on your body as you can by tailoring the ball specs to your hand.
When looking for shoes, I suggest Linds, Dexter, or ABS. They are more expensive but it pays off in the long run because they don't seem to break ever. You'll probably end up replacing them because you're tired of them and want new shoes before actually wearing them out.
Go to
www.ballreviews.com. It's a very comprehensive forum discussing everything you need to know regarding bowling. I was once a very active member there before I discovered CPF. It's been months since I last visited there.
Be careful, being a flashaholic and a bowler at the same time is very costly because they're both very expensive hobbies. Trust me, I've been bowling more than 10 years 2 to 3 times every week and I can't even get past the mid level stage to the serious competitive stage due to budget constraints. Having all the newest and coolest equipment won't do you any good if you don't practice and bowling requires lots of practice. Remember the pros who're averaging 200 above usually practice upwards of 40 games a week. Discovering CPF last year hasn't been of any help to my game and has actually made the situation rather worse for me but I'm not willing to give up either one.
Don't get me wrong. I'm not trying to discourage you from jumping into this but you better be prepared for some serious commitment or you'll end up with more frustration than you bargained for. But then again, if you don't mind being stuck with averages in the 120's, you should be fine however little time you can devote to it. But if that is the case, why bother purchasing your own equipment? The main purpose to do it is to improve.
Good luck.