You basically have three options: a mask, RMG (Rubber mask grease paint), or airbrushed makeup. Each has benefits and drawbacks.
Mask:
Benefits are no runny makeup and scare factor.
Drawbacks are limited peripheral vision and you get a lot hotter.
RMG:
Benefits are a lot less runny, tends to last a long time, as well as you have your peripheral vision, so you don't run into as many things.
Drawbacks are that if you sweat profusely, it can still run, and depending on the brand, you have to have a special type of remover.
Airbrushed:
Benefits are that it almost never runs, can look super creepy, and is very durable.
Drawbacks are pricing(airbrush makeup systems can run from $75-$1,000+), removability, as you need a special remover to take it off, and tendency to cause allergic reactions in people with sensitive skin.
Having used all three of these methods, I suggest going with RMG, unless you can afford an airbrush system.