I would say it depends on what platform you want to shoot them out of.
If you want to use a gas gun (AR) or a bolt gun, then the obvious choice is 350 Legend mainly due to availability of firearms and ammo. You will get better performance (IMHO) than the .450 and as far as I know the .450 is only available in gas guns and single shots.
If you plan to go with a single shot (break open or rolling block), then your choices go up quite a bit. I am a fan of the .357 Max if you plan to use a break open single shot (Contender/Encore/Scout). With that cartridge you will get performance on par with the 350L, but have the ability to use .38 Special or .357 Mag ammo for plinking, small game, or short range big game. Using a single shot also opens up more of the "vintage" cartridges that fall into the "straight wall" category, such as the 38-55, the 375 Win, and the 32-40.
Of course you always use the .300 BO. It does a great job on deer in both the super and sub-sonic offerings, provided you keep the shots in the window of acceptable bullet performance.