I'm throwing this for a loop - Some of the best (although very few because the "trend" right now is that "bigger is better") jumpers I've ever seen have been 15.1-16 hh, so don't automatically think that you NEED a horse to be over 16hh to jump big. Smaller horses can collect up much easier than bigger ones, which makes a ton of difference.
In all honesty, you're probably going to go through a couple of horses before you reach your 6' goal - most Grand Prix horses (the 5' jumpers and up) are in the six-figure range as far as the price sticker goes. If you're only jumping 3' now, chances are your next horse won't be GP caliber.
Start looking for a 3'6" - 4' prospect or seasoned jumper.