Why run Cat6, when if cabling is correctly installed, Cat5 will support up to GigE throughut with no problems, (up to 100M) ?
Cat6, (even Cat5E and Cat7 as some vendors call their cabling), has only been proven necessary when around severe electrical interference, such as run over flourescent fixtures, or high-voltage/amperage lines. And even then, no cabling should be run over these conditions, except fiber.
Nothing in a standard home wall should require the use of Cat5E or above. Cat5 is fine.
Also, Cat5, 5E, 6 and 7 does not only refer to the wire. You can reduce the level of a "Cat6" wire to less than Cat3 if crimped improperly, or too many twists are removed at the crimping point.
And please do not cut off the 4 wires you "think" you do not need while crimping the connector on to the wire. Bye bye Cat5, 5E, or 6.
Also, do not make two connections, eitehr two ethernet or one ethernet and one/two telephone connections out of a cat5, 5E, 6 or 7......again bye bye good ethernet connections.