I'm looking to max out my character move speed for running through levels fast (not necessarily clearing enemies or doing high difficulty runs), but I can only find guides on the "fastest leveling methods". Which character build is the fastest, or are speeds about equal on the fastest build for each character? What are the best builds for speedrunning?
I haven't completed speedrun myself, but there are several options for DH Vault skill
1. The best option.
Currently nearly all DH builds are using cubed Dawn and ideally 38% cooldown reduction on gear (you don't need that much, 20% works pretty well), which let you have constant Vengeance for a massive dps boost. If you use Seethe rune, then it's +10 hatred/sec, letting you cast Vault nearly non-stop.
This works with any build, but have a look at this particular one, it's not the best for GR (grenades skill doing relatively low dmg output), but it's the most mobile one (don't forget to use Seethe rune!) and give huge survivability (due to ability to keep mobs stunned and infinite vault).
2. Good option
Using Chain of Shadows belt will make Vault free for 2 seconds (2-3 casts) after using Impale.
You will need again cubed Dawn and Vengeance with Seethe rune to cover high cost of Impale, but that's all you need.
Impale, Vault, Vault, Vault, Impale, Vault, Vault, Vault.... you should have an idea.
P.S.: among quick travel options Teleport is the best, you don't need to open doors, you can jump over obstacles, distance is the biggest, so for best results I'd look into it, though I don't have experience with it, let's wait for some sorceresses/monks here ;)
P.P.S.: As DH I can easily outrun any crusader/witch doctor, so I recommend you don't look into those as they are considerably weaker.