Hey, Matt. Couple of things. First, the board length rule of thumb assumes you are of average weight for your height. If you're heavier, lengthen the board a bit. Weight is actually far more important than height. Most boards have a size chart. If they specify weight and height on the chart, give priority to weight.
Second, generally speaking higher price gives you things like better quality ratchets on the bindings, better padding underfoot, extras like canting, highback adjustment (sideways), quality in general. Same idea with boards.
Third, if your budget is such that you have to make compromises, then spend the most money on the boots. Bad-fitting boots will ruin the experience faster than anything. And heel-lift will just kill your turns.
Last, ask yourself two questions: 1) How certain are you that you'll stick with snowboarding, and 2) what kind of riding will you do?
If you're just giving it a try and you may or may not stick with it, just buy a used board and bindings, until you're sure you want to stick with it. If you're not sure about #2, same answer. Once you decide what you want, definitely spend the bucks to get good equipment. It does make a difference once you're past noob stage.
In retrospect, "Let's get the goat drunk"
should have been my cue to leave the party.