If you're looking to get into PlayStation emulation purely for speedrunning purposes, then BizHawk is your best bet. While it's lacking in features when compared to its rivals and only runs at native resolution, Mednafen's PlayStation core boasts a very high level of accuracy and game compatibility. Some of its cores are ports, but many have been coded from scratch and are famed for their compatibility and accuracy. Mednafen – which stands for 'My Emulator Doesn't Need A Frickin' Excellent Name' – doesn't just emulate PlayStation, but covers a whole host of retro systems.