Remember that a rental shop will almost always put you on a board at the smallest end of your weight range. The best way to get sized up for a snowboard is to head into your local snowboard shop (not a big box store like Big 5, they don't know what they're talking about) and talk to the folks there. The length of a board has very little to do with how tall you are. Your weight, ability level, style of riding and the conditions you ride in all play a role in the length of board you choose.
By far, the most important decision you need to make is about your boots. Spend the most time here and if need be, the most money as well. Never buy the first pair of boots you have tried on and don't sacrifice comfort or performance to save a few bucks. There is nothing worse than boots that don't fit right. As far as fit is concerned, if a boot fits perfectly in the store then it is TOO BIG. A perfect fit is one in which you would think to yourself "If this boot were a bit bigger it would fit perfectly." Boots stretch after a few uses and you don't want your feet to be swimming in your boots.
As far as costs are concerned, snowboarding is expensive. There are definitely deals to be found but you can spend anywhere between $500 and $2000 just on equipment. Boards cost anywhere between $300 and $1000, bindings $100 to $500 and boots can be about that much as well. Remember, don't skimp on your boots and also don't forget to save some money for other important items. Items like gloves, goggles, pants, jacket, long underwear are very important. You could have the greatest setup in the world but may not be able to enjoy it because you can't see and are soaking wet.