Welcome to Just Answer! My name is Maverick. I very much enjoy what I do and I hope that you will benefit from this information.
It appears that you would need a class B or a specialty class C license to do the residential remodeling depending on the scope of your remodeling work. The class A is more for engineering type work as follows:
"A" General Engineering
A general engineering contractor is a contractor whose principal contracting business
is in connection with fixed works requiring specialized engineering knowledge and skill,including the following divisions or subjects: irrigation, drainage, water power, water supply, flood control, inland waterways, harbors, docks and wharves, shipyards and ports, dams and hydroelectric projects, levees, river control and reclamation works, railroads, highways, streets and roads, tunnels, airports and airways, sewers and sewage disposal plants and systems, waste reduction plants, bridges, overpasses, underpasses and other similar works, pipelines and other systems for the transmission of petroleum and other liquids or gaseous substances, parks, playgrounds and other recreational works, refineries, chemical plants and similar industrial plants requiring specialized engineering knowledge and skill, powerhouses, power plants and other utilities plants and installations, mines and metallurgical plants, land leveling and earthmoving projects, excavating, grading, trenching, paving and surfacing work, and cement and concrete works in connection with the above mentioned fixed works.
(B&P Section 7056)