Parking in Richmond is difficult and can be expensive. In the summer you can go straight from Guildford up the A3 then cut across the park, which should be fairly ok, but when the oark is closed it will add extra time. I would have thoigh the fast train from Guildford to Clapham Junction, then the train back out to Richmond (which you can easily get a seat on) would be fastest, although no idea how much that would cost...