Type A is driven from the output of the existing ballast and consequently has significant compatibility issues as well as creating a dependency on a working ballast and the innefficiency of multiple conversions.
Type B works from mains voltage wired into the existing sockets and has the attendant safety hazard of high voltage.
Type C uses a switch mode current source mounted in the fixture and the light engine (tube) has no hazardous voltages.
I would only use type C; they're the safest and most efficient.
The ones we use here are similar to your last unit. Starter is replaced by a unit containing a 200 ma fuse. Internal driver in the end of the tube, balast remains as no longer required but pia to have to rewire to remove it as it has no effect.( not required)