What kind of GP do you want to do? Do you want to be correct, but not necessarily competitive or are we talking about national and international level?
For the former you do not need a million dollar horse. Although, for any horse, the initial investment is inconsequential compared to the continuing costs of keeping a horse.
I'm just about to FEI now but my changes and tempis are just not there. I train full time and I have had the opportunity to ride many types of horses from all levels. My current "good horse" is a 13 y/o 17.1h TB that really does look like a Warmblood. Unfortunately he doesn't move like one, but he will go all the way to GP. He has all the movements, he just has to put them all together. I had a 9 y/o Arabian problem child that was athletic enough to do GP, but maybe not the mind for it. I have had many that were not ideal dressage horses that could easily do 3rd level work (if not more) including QH's, TB's, Morgans, and Arabians. And mind you, not all Warmbloods will have the athleticism and work ethic to make it to GP.
That being said, if you get a good enough eye, feel, and get to really know horses, you can pick out a prospect and bring it along yourself if you don't have money. If it doesn't work out, you sell it and buy something else. If you did a good job, got it up a couple levels and it's not crazy, you will get your money back and then some. Reinvest! It's not the perfect way to get to the GP, but it's not a perfect world and there is no perfect horse.
As a side note, I've had more trouble with keeping horses sound (mostly due to accidents!) than horses that simply cannot do the work. This is the sad part with horse ownership. You can be stuck with an unsound horse and thousands in vet bills, facing very hard decisions. Make friends, get your face out there, and network. You never know who you are going to meet or what sort of opportunities might come your way.
Finding good instruction is hard. In some areas, impossible! Good instruction is expensive. I decided to take up a part time working student position with an FEI trainer to step up my game. I really think this is where people that are truly dedicated to dressage get hung up. It's not just about finding someone that rides GP that gives lessons, it's about finding someone that rides GP correctly that gives lessons that can connect with you. Since everyone learns differently, it's not a one size fits all situation.
I am taking my dressage journey one level at a time. Perfect the level that you are at, play with the things just beyond, but don't get lost in the tricks. Enjoy what you have and what you can do.