My new yard seems to be all clay, water just runs off, some areas are flat areas and some a little hilly, so it washes everything off in rain, should I rototill and add something? And what is the best grass to grow?

Sounds like you just need aeration. Heavy clay soil yards ought to be aereated twice a year. You can try something like this, but best results are with an aerator.

In my area the rental on a good aerator for the day is the same price as having someone do it for me.

Don't mess with whimpy ones like this, make sure it's done with a commercial gas powered one or one pulled behind a tractor that will pull out 1/2 to 3/4 inch plugs.

Apparently, buffalo grass is the best grass for growing on slopes. You will still have to deal with water run off unless you try another option such as putting in terracing and planting groundcovers.

Clay soils are rich in nutrients but have to be aerated more regularly. You might try adding gypsum to break up the clay mixture and improve soil aeration..