The A35 is a mixture of single and dual cwy stretches, A31 2 lane duals.
If traffic is moving will take 1hr 20mins to reach M3.
Other routes very scenic, mainly windy single cwys with not many overtaking places so you could get stuck behind slow moving stuff.
Salisbury at the wrong time of day can be a pain to get around.
On Bob's last suggestion the A303 runs into the M3 at Popham
Check Google Maps traffic before starting to see if the fast route is ok.