You'll have to do the math to see, financially, how many days of use you need to put in before the cost of ownership pays off. Don't forget to include boots and bindings in your figures. And, if you're young, as it sounds, you'll need to estimate the number of years of use you'll get out of your own equipment until you outgrow it. If you only ride a few times a year, renting certainly will work out cheaper.
Beyond cost, the cons with rental boards are their typical low quality, poor maintenance (ie; waxing), and questionable availability in your size. Of course, it can be a hassle to stand in line and get fitted every time you hit the mountain. Owning your own gear certainly is nicer, but remember that you'll need to learn to wax and maintain it (or pay a shop to do it instead).
If the cost difference works in your favor, or at least is close, then IMO, it's time to consider buying. Don't overlook the used market for equipment. There is tons of great gear on sites like this and ebay, that can be had for a fraction of the new price. Of the half dozen boards I've purchased over the last 18 years, my last three boards (and another in route as I type), were used, in fact. With the exception of this last one (an '08 model in mint condition), all cost less than half the new price.