A3 is best avoided, mainly because of Hindhead although it's longer anyway.
You have a few options (check them on a map to save me giving loads of detail here):
M25, M23, A23, A27
M25, M23, A264, A24, A280, A27
M25, M23, A264, A29
M25, M23, A264, A24, A283, B2139, A29, A27
M25, A24, A29, A27
There's not much in it time-wise but I'd probably go for the last one. You go around Leatherhead and just touch the edge of Dorking. Then pick up the A29 at Beare Green to take you to Fontwell. Then A27 to Chi. Some great views of the Downs too.