I wouldn't hire it costs a fortune! Buy a board.
As said before get good boots, they are key. Badly fitting boots are dangerous! I borrowed a pair of boots the first time I went snowboarding, the board was too advanced for me as well. I went bombing down a slope on my first day, hit a bump, went flying and landed so awkwardly I tore the ligaments in my leading foot. Still determined not to ruin my holiday I hobbled out and rented some better fitting boots and carried on for the week.
If you're learning make sure you get some impact shorts, you're bound to hit the deck. As said before indoor slopes are boring unless you're big into snow parks, even then they can be somewhat limiting so get out to the alps.
As for destinations the last place I went to was St Anton in Austria, great apres as well but if you're new I wouldn't advise getting in the party spirit, sinking a few pints of the amazing white beer and heading down the slopes, you will take a tumble as you can see the bars on the slopes get pretty full at 5pm:
I think I'm off to Ischgl in Austria next january, can't wait