For a cheapish place to stay try here
http://www.moanalodge.co.nz/ I'm here at the mo whilst looking for jobs in wellington, its about 20 mins from the city centre by train in a small village RIGHT on the seashore, very nice quiet relaxed atmosphere and very clean. We were staying in the city centre at the worldwide backpackers which was okay and nice and central but out here might suit someone serious about job hunting better and I couldnt recommend it enough...
I'm looking for tech support roles as well and to be honest id say dont bother applying for anything until you're here, they wont bother with you until you're in the country and available for interview. Have only been applying for stuff since last week and only for contract roles so have to see how it goes this week with actual interviews. I also havnt tried any fulltime or company roles yet, just recruiters.
Also I'd say just grab a simcard in any vodafone or telecom store when you get here, they're NZ$30 with $15 free credit when you register.