hi wvrius,
I think Jesse's suggestion and approach is a good one, albeit somewhat advanced for a "noob", but it nicely illustrates the power of parameters.
The nice thing about any CAD system is there are always multiple ways to achieve what you are trying to do and the more experience you have with them the more effecient of a modeler you'll become, don't be afraid to try different approaches.
So I wanted to go back to your original method.
"One solution I thought of was: create an offset plane from the non-rounded face, and position it at the max of the curvature. Then create a sketch on the plane and place a circle where I want the hole to start. This approach seemed to have worked, but doesn't parametrize well - the offset plane is not 'attached' to the body. So if I'm moving or scaling the body, the offset plane and attached sketch do not move."
Your thinking on this was right, but the tools didn't quite match what you were expecting, so I wanted to show you an alternative that would work the way you were describing or at least expecting.
In three easy steps I was able to create the scenario you described above, and this could have been done in two step, but I wanted to illustrate how construction planes can work for you.
after createing my base shape;
1. create a mid plane construction plane, select the two outer parallel faces. once the center plane is created if you update the main shape by editing the sketch, the plane will stay centered to the geometry.
Note: this is the step you could eliminate if you built your sketch for your base feature centered around an origin plane, that way an origin plane is always at the center of your design.
2. create a sketch on the midplane, use project and select the face of the arched end of your model. This creates the points at the extent of your arch and parallel to the two sides.
3. create a tangent to face through point construction plane, select the arched face and the point at the end of the sketch
Now as you change the parameter of your first sketch, the construction planes will update as you expect, keeping that tangent plane "attached" to the body.

remember this is just one approach to getting the results you want and this particular approach helps ilustrate how construction geometry ties to the model. YOu could get here in one feature using the tangent plane construction plane (as apposed to the Tangent Through Point above), but you'll need to do some fine tuning to get the precise result you want.
hope this helps and I'll post some models later today to share with you showing a couple different aproaches.
hope this helps,
Jamie Gilchrist
Senior Principal Experience Designer