What type of wire should I use to feed a 70 ampere subpanel?
The wiring will have to be in some form of raceway the entire run. If you're using Non-metallic sheathed cable, the jacket fulfills this requirement. If you're running individual conductors, you'll have to use conduit or some other approved raceway.

As for conductor size. If you can meet all the requirements for using the 90&deg;C column, you'll be able to use 6 AWG copper for the run. However, since you're less than 100 amperes, you're likely going to be using the 60&deg;C column. This means whether you use single conductors or a cable assembly, you're still going to have to use 4 AWG conductors.

NOTES:
 - More information can be found in my answer to this question: What wire gauge do I need for a 100 Amp subpanel at the end of a 60' wire run?

 - After further research, it appears 75&deg;C is common for load center terminals (check your specific equipment to be sure).