So, I've been doing some digging, and I found that the chamber pressure for the raptor engine is more than 4 times that of Merlin (~4,000 psi to ~980 psi). How would SpaceX manage to pressurize the fuel/oxidizer enough to be efficient? And if they're planning for their liquid methane to be self pressurizing wouldn't that take too much of the fuel supply?
From the wording of the question I suspect you think the entire fuel/ox tanks are maintained at higher than the chamber pressure. They're not: tank pressure is a few bar. The fuel and oxidizer are pressurized in the turbopump.
Self-pressurizing means they have to boil some of the fuel (which is easy, when you have a rocket engine providing all the heat you could possibly want) and run the gases back into the tank. This means some of the fuel is not available for combustion, but it's more efficient than the alternative: a heavy tank (strong enough to withstand ~200 bar) filled with enough helium to fill the entire fuel tank at a few bar.