I personally think Ian could do the job, no problem, and probably do it very well... something we'd all likely praise if pics were posted.
I have no doubt your work would meet and exceed NEC code requirements, and be very neat and workmanlike. But you should research local codes as well. For example, here in NYC local code requires #12 on 15A circuits.
Iwire makes a good point though that some municipalities won't even inspect [and approve] howeowner work. In order to get that permit, it might have to be applied for by a licensed EC and work done by a licensed EC. Here in NYC, short of replacing a light bulb, a homeowner can't do ANY electrical work... or plumbing work for that matter.
Ian, it appears your parents want you to do the wiring. Obviously, they have great confidence in your abilities. That home is the biggest investment your parents will ever make, so you should consider it a sincere compliment that they would entrust you to do this kind of work on it.
If your parents absolutely refuse to pull a permit, and you'd feel better if someone physically looked at your work, if you're friendly with a local electrician in your area, perhaps you can have him (or her) "inspect" your work... just don't expect them to give you anything in writing. Also don't be shocked if they find your work perfect... I wouldn't.
Joe
