I'm sorta the same way, so I know how you feel. One thing, DON'T DELETE IT. I don't care how bad you think it is, don't delete it. If anything, add another layer and fix the mistakes you see. You'll eventually train yourself to do better.
Also, your arc doesn't have to be one stroke. Feel free to go over it 5 or so times till it comes out how you want it.
Think of this as a sketch, make it as a basic idea, it can be really bad but give you enough detail to do the next step. Once that first piece is down, then you can sorta retrace your work to get that smooth lined look you're trying to achieve in your picture.
I like to think of the sketch kinda like clay. Want her cheek bone to be higher, then move it, don't trash what you have cause of one (or more) issue(s).
Also learn to draw with your eraser. Use it to carve out details instead of just removing what you don't want.
I like to use Autodesk Sketchbook Pro. It's a very simple interface and, I feel, it let's me sketch easily without being distracted by things like masking or whatnot. Brings me back to the days of me and my sketchbook.
It really depends what you want to do with your art from them. If it's just a sketch, you're done. If you plan to really color it or something, GIMP should do fine. Honestly, I've seen beautiful works done in programs other than Photoshop (like GIMP for instance), so don't worry about what program you are using. It's more how well you know the program, not which one you use.