You can never go wrong with using slate. Some members even get it cut large enough to use it as a tank bottom.
I agree to some extent, however be aware of the source. Fine grained sedimentary rock like slate and shale are notorious for containing high amounts of naturally occurring hydrocarbons dependent on the source. That is, they can leach what is basically crude oil into your water. Red slate contains high amounts of iron and other metals, so it to can be problematic for some set ups. A simple "smell test" can provide you with what you need to know for hydrocarbons. Simply break off a piece of the slate and smell what geologists call the "fresh face" If it stinks like anything other than nothing, avoid using it. My favorite source for slate is the scraps from a local counter top shop. (I get them for free!)
One type of rock that I think you need to steer clear of is limestone due to the fact that it will increase your PH. At least I think that's the case, if not, someone else will chime in and correct me.
Limestone should definately be avoided due to pH changes, it is naturally very alkaline.
My personal top reccomendations are medium to fine grained granite, quartzite, sandstone, and water polished marble.
Avoid any rock that has naturally occuring green colors in them as this is most often various forms of copper which can leach into your water.
One option I use for an extra safety net is to brush on a thin coat or two of epoxy or urethane to seal the rocks completely. It may take a few coats on especially rough rocks, but the advantages out weigh the time spent doing this. First and foremost the sealant makes vivaria cleaning a snap, second, it gives the stones a pleasing wet look,that enhances the natural colors in the stone.
Vid is also correct, avoid anything with sharp edges.