I have no idea at all of the rules for flying a jumpship in the USA, but in the UK it's as stated above - i.e. you can fly a jumpship or a tug, but not be paid for either.
Being a skydiver you'll find will help you a lot. I'm a former skydiver myself, and have flown various jumpships - Islander (piston & turbine), C210, Turbine Porter among them.
You'll need to do quite a few trips with an jump pilot instructor/examiner on each aircraft type (if the rules in USA are the same as UK) before being let loose on your own.
As you're probably aware (depending on your jump experience) different jump types require very different skills from the pilot.
For dope ropers all you need to do is hold it steady at low speed for a couple to get in the door and exit.
Style (or 1-way RW

) is also quite simple, but you need to follow RT instructions to the letter for the run-in over the cameras/telemeters. Call "Standby Standby" and "Exit Exit Exit" to the jumpers before acknowledging the call to the ground.
Hardest of all to fly is RW and any form of launch. You'll have them crawling all over the outside of your aircraft, mucking up the airflow and wondering if they look cool enough for the camera for ages before you can remove them and head for a cup of coffee. All that time, of course, you're close to the stall with low power set. I believe there is a video on YouTube of a BN2 stalling and then spinning with skydivers attached to the outside.
Be prepared for the CCI to want you on the ground 5 secs after the drop. If flying a piston, beware the Chief Pilot berating you for shock-cooling an engine or encouraging piston slap for coming down too fast with not enough power on. Remember - sideslipping is your friend.
If you lose the OP and they have to come down with you, be ready for it all to be your fault - even if cloud cover is 7/8.
Flat turns on the run-in are order of the day - use loads of rudder and opposite aileron, then gradually uncross the controls. Worst is the jumpmaster who calls "5 right - 5 right - 5 right - 5 right..." and you don't get a chance to uncross.
Finally, if flying something like a C210, KEEP A SPARE KEY ON YOUR PERSON. Sooner or later some d1ckhead is bound to think it's funny to lean over you, remove the key, and go out of the door with it.

This happened to me. But I got my revenge.

On our next lesson, we'll cover how to put someone out of the door 5 miles short of the DZ...