we've got excellent broadband, with iinet, but it does depend where you are and what services you can get. We're on their 'NakedDSL' and also have Fetch TV. our phone is VOIP through their system and we get cheap calls back home as well. They've always been really good, we've had excellent customer service, so I do recommend them if you can get them.
I agree with Neal - get a medicare card asap, get a driving license as soon as you have a fixed address (you'll need to take in the tenancy agreement), and get a TFN (you can walk into the ATO office in civic and do it in 5 minutes, they'll post it out to whatever address you provide).
And, yes, Canberra's a great place to live if you have somewhere short term to stay for a few weeks it's worth using that time to explore both sides as I find there is a very different feel between the north and the south, as well as investigating schools, childcare etc, so that you can see what will suit you best.
Be prepared to apply for longer-term rental places on the spot as you see them (I heard people say it's worth making up an application pack with references, bank info to prove you have the income if you don't yet have jobs, that sort of thing - we did that, and it also meant I usually had the info available for filling out applications as needed). Competition is often fierce and if you can get to weekday viewings you're likely to be a lot less crowded out. Some of the Saturday viewings we went to would get 20-30 couples in, and maybe 10 of those would apply for the house at the viewing. Admittedly we were looking in February when the rental market tends to be at its busiest!