What type of rock will abrade the fastest?

Well that really depends on a lot of different factors. For example, limestone or marble will abrade extremely quickly in a wet environment where it is exposed to rain but in a place that is dry (like Egypt) limestone (the stuff the pyramids are made out of) will last for thousands of years.

If you are talking about a "type of rock" as in the standard, igneous, sedimentary or metamorphic classes, I would say sedimentary rocks will abrade faster as they are much weaker.

If you want a name of a specific rock, in general, softer rocks will abrade faster than harder rocks. You measure the hardness of a rock (or of anything really) on the "Mohs Scale". Diamond is considered the hardest at a 10 on the Mohs Scale and the softest rock of all the rocks, scoring a mere 1 on the Mohs Scale, is Talc. So talk can be abraded by even your fingernail.