Overgrown hedge needs replacing- Where do I start?

[karise]

Old conifer hedge was planted too close to the boundary footpath. It's one of those that doesn't grow back when you prune it (don't know the technical name).
Need to take it out and replace with something which is prunable. Where do we start? Needs to be at least 4 feet high from the start as it's a busy road so needs to take a fair hammering! Is it going to cost a fortune?

Forgot to say- it's 12 feet long..

You could have a look here, there are lots of types of hedging plus descriptions and prices.
www.hedgesdirect.com/