I think this is a great idea, I've riden all sections from London to long buckby along the Grand union. For me, it's a fantastic way of seeing loads of different scenery and architecture without being on the road.
A word of caution though, as has been pointed out previously, the tow path can be pretty rough in places, usually once you get away from towns and cities. Also practice mending punctures and minor maintenance as you could end up having to push your bike rather than ride it quite away if you have issues in the more remote areas.
Time wise, I would say about a week should suffice
Training wise, just ride your bike as often as you can, shopping trips, to the pub etc.
As for accommodation, why not camp, that way with care, you can stop pretty much when and where you fancy. I'm lead to believe pub gardens are good for this
Whatever you decide, keep posting your progress and best of luck with the trip.
If it does go ahead in may, you may come across a group of us doing our annual Milton Keynes to birkhampstead canal side pub crawl (we'd even buy you a pint)