Binos,
Option one above may be awkward as the Billion is already a router! Adding a wireless router to that can cause some fun as your addresses get translated twice. Best to plug a Wireless acess point in to the Billion if you really want to keep it...or use option 2.
At the risk of muddying the waters even further....
Have you considered an Iburst setup. this is a wireless broadband setup that works in BNE/SYD/MEL/CBR (but sadly not PER). See
Iburst
Basically it is a box (or a PCMCIA card...more expensive) that lappy can access net from without telephone lines. One BIG adavantage is when renting you can move house and take it with you.
I have one setup in BNE with a wireless router attached in the hotel where our crew stay. anyone wth wireless can connect and if we move accom I just move the box. No transfer/setup fees!
Shop around for an ISP as there are a few. Ozemail, Chilli, are 2 I have used.
If you already have ADSL connected then it may be too late. But worth considering for any renters.