What type of cable should I run from the service pole to my house for cable internet?
The price you've been quoted sounds as though they are going to pull feeder cable from their tap location. Feeder cable is typically 0.500 inch nominal outside diameter, frequently larger when including insulation and in the case of underground rated cable, a goopy substance used ostensibly to seal nicks in the jacket. 

The stuff is seriously stiff, but can be pulled through conduit if the conduit is large enough diameter and uses sweeps at each end. Go beyond two sweeps and you may run into trouble.

Considering that you want to provide the labor, conduit is the correct way to go. Should you find yourself digging in the area in the future, a clunk of the shovel against PVC is preferred to a gash in the cable.

The cable company will likely provide you with the cable, called five-hundred, if you explain that you'd like to put in the conduit and cable in one sequence. They would suggest that you leave a few feet at each end for creating the terminations.

I've dug up too many feeder lines for repair purposes to say I enjoyed myself, but I had a good reputation on the device used to locate the break that the digging was more localized. With conduit, even if you drive a back-hoe blade through it, the need to repair becomes immediately obvious.

At the price you've been quoted, I'd guess that you have more than a couple hundred feet to travel.