The number of choices in this game when it comes to characters and builds are quite immense. However, just like in any game, it is not perfectly balanced, and some characters will shine out more than others. There are many categories in this game and, therefore, there is not one definitive best character, but there are some tendencies:
Traditional speedruns: Peddler Peddler is an incredible character. He is noted for having the best one-shot skill in the game, 1000Kg Swing, which can vaporize bosses in one hit with the right item build. However, this is not his strongest attack for speedrunning: since most of a runner's time is spent going through regular rooms, 3/2-1 as a build will generally serve as a far better option, since the low cooldown of this swinging kitty variant combined with its enemy-pulling vortex will wipe out rooms very quickly. Its lowered damage can be remedied by using skill 1 as a secondary, and although this combined with the armor loss makes for a very risky set, combining it with an HP regen item (namely Dracula's Dentures) will make it safer to use.
As a final point, Peddler also has a fast movement speed, making him good in Any%, where the Optical Camouflage will be used and running through rooms quickly will be an advantage.
NWRs: Hannah Hannah is a character that has a good deal of useful attributes for a NWR, namely range, overall pretty high damage and good crowd control potential with 2/3, and lots of mobility, which allows for a conservative playstyle that is perfect for NWRs. You can also compensate her somewhat slow attack speed by using a boss skill to aid you in that sense, Tiger Jump being one of the best due to its low cooldown and incredibly high safety. Other good picks are characters with safe skills that involve very little commitment, like Peddler (again) with his Whirling Blow, or Katherine with her Glacial Tempest. The most important part in a NWR is being able to avoid taking too much damage so that finishing a run in the first place is possible; killing enemies quickly is just an add-on.