If you want to compare the ASB rate to someone like HIFX just call them both and ask.
You can open a bank account with any of the NZ banks from the UK - see the links on their websites. We faxed the Westpac form to them in Auckland one day and the following day we received an email with our account numbers etc. You are then free to shop around for the best rate. If you like the look of ASB then open the account with them but don't given them any money straight away. Once again you can then shop around.
I would guess that the ASB rate would be slightly worse than HIFX, Moneycorp, Currencies Direct etc. ASB also charge a transfer fee I think.
When you get to New Zealand go into a migrant branch as soon as you get there. They will need to see ID and then they will activate your account and give you your EFTPOS/ATM cards on the spot - no waiting for the post.