There are actually 2 terminals at BHX, and the cable car to the train station only goes from Terminal 2. They may have moved the car hire desks, but they used to only be on the ground floor of Terminal 1.
A big agreement to stay far far away from the M42 (and all Birmingham motorways) at rush hour. Traffic tends to be distributed all over the city, not just all into town in the morning the reverse at night. The M42 was one of the demonstration areas of the variable speed limit, the traffic is so bad. Off peak it isn't too bad, if you are used to city driving. A45 out of BHX to M42 southbound to M40 southbound to A46 southbound and off towards Stratford upon Avon, follow the road around the one way scheme, over the bridge first right and follow the sat nav for one of several routes.
Heathrow to M4 extension to M4 to A34 towards Oxford (watch the reduced speed on the southwest side of Oxford) to A40 towards Cheltenham to Burford, Stow and Chipping Campden
Or Heathrow to M4 extension to M4 to M25 northbound to M40 northbound, to through Oxford on the A40, see above, or off the A40 to A44 on the west side of Oxford, and through Chipping Norton, Moreton in Marsh to Chipping Campden.
Or if the M25 is plugged up, M4 extension to M4 to A404(M) to A404 to High Wycombe to M40 northbound and as above.
Use your sat nav.