When you say Continuous Sampling' I would have a couple of comments, in addition to the above.
I will assume you are not using the CME Continuous Sampling system with hollow stem augers. The quality and anticipated use of the samples will open and close your options.
For good quality samples, assuming the soil conditions allow, I have sampled with:
1) 1st a Shelby Tube (12"+ as possible) followed with a SPT (24"), cleaned with auger to near bottom of SPT, followed by the Shelby Tube & SPT combination, to total depth. The SPT will fit in the Shelby Hole with minimal sample disturbance. The Shelby which follows the SPT will include the soil disturbance in front of the SPT and should continue into relatively undisturbed soils.
For good to atrocious quality samples, assuming the soil conditions allow, I have sampled with:
1) 1st a Dames & Moore Spoon(24") followed with a California Spoon (24"), followed with a SPT (24"), cleaned with auger to near bottom of SPT, and repeat until the driller's arm falls off.