There are many web pages on spiders out there, although very little on New Zealand spiders. Perhaps the best site to start with is The Arachnology Home Page as this site includes an impressive list of links to spiders from other parts of the world.
You may notice that a number of the species covered on Te Papa's website are Australian species that have become established in New Zealand. If you would like to know more about these spiders in the context of their native Australia, here are some links to Australian spider websites:
The NZ National Poisons Centre website including advice on treatment of bites
http://www.toxinz.com/
Landcare Research's bug identification site, including a few spiders not covered on this website
http://www.landcareresearch.co.nz/research/biodiversity/invertebratesprog/invertid/
Museum of Victoria spiders page
http://www.mov.vic.gov.au/spiders/
Australian Museum spiders page
http://www.amonline.net.au/factsheets/index.htm#spiders
Queensland Museum spiders page
Australia's venomous creatures page (including a section on spiders)
http://www.pharmacology.unimelb.edu.au