If you just want an email server, then it's hard to beat Gmail. We have talked about this many times haven't we 
Once you have the UDAI from whichever company hosts your domain, you need to get them to route all email from your domain to some Gmail accounts that you set up -- one for each address in front of the @ symbol.
All of the Gmail side of things is free, but you will have to continue paying somebody to be your domain host. If you don't like your current provider, I can recommend a good yet very economical one in the US. However, this won't be any good for a .nz domain. If that's the case, I've not heard anything bad about Planet, so probably a good idea to give them a try as RaeM1 suggested.