You should look around and see what is available. You shouldn't set yourself on a breed. With that kind of money I doubt you will find anything but a cross bred so the options you put up won't work anyways.
Look around for a horse that matches your experiences and riding level, then consider the breed when you find something that moderately matches what you need.
Of what you posted, you won't find a welsh pony for less than 3,000. Not where I live anyways as for the australian bred I'm not familiar with and the QH well, I think it's a much more realistic breed. Every horse is different and not all QHs will be suitable for you but there are certainly many of them around. I have no doubt in my mind you might find one that works well for you.