Even if you're having a new house built, you get a lot less choices than you might think. To most builders, "custom home" means you get to pick the paint and flooring, not that you have appreciable input into anything structural.
I'm sure it varies regionally, but where I'm at (Kansas City market) you have to be in about the $800k range, generally, to be able to work with an actual architect and build something custom - and that's just plain out of reach for most people.
I know, but I was assuming the OP already knew they had the opportunity to dictate the architecture of their house, since that's what they were asking about. Either they have money or they have volunteer labor and low expectations.
I'm sure it varies regionally, but where I'm at (Kansas City market) you have to be in about the $800k range, generally, to be able to work with an actual architect and build something custom - and that's just plain out of reach for most people.