I know this is an old thread, but this may be of use to someone else in the future....

I teach guitar privately. Normally around £10-15 per half an hour for a one to one. I wouldn't recommend the DVD/internet route for kids. They need someone who can give them feedback, encouragement and ideally play along with them. Self tutoring is very hard and in my experience, they lose interest quickly. If there's something that they are struggling with (which there will be regularly) then you can't beat the personal touch.

Having said that, I realise that it is an expensive hobbie and I'd thoroughly recommend trying to do it through the school as a cheaper option. There are plus and minus points of this. Playing with other people is great fun but you obviously don't progress as much as you might with individual lesson plans. I loved learning at school but feel I would be a better player now had I have had private lessons.....