Honu,
The other alternative to staying in Canberra, is staying in Queanbeyan - which is just next door to the airport but actually in NSW.
A couple of cheapish suggestions from my years in living in Canberra and regularly commuting - Olims, right near the city centre and easy access to the airport and Motel Monaro - in Kingston and not far away at all. You should find both these hotels on wotif.com.
I'm not sure that any of the hotels in Canberra have courtesy buses (although I stand to be corrected) but taxis are really reliable - I've caught 50+ early morning taxis to CBR airport and never had any probs.
A word of warning though for your flights, Canberra is notorious for getting 'fogged' in during Winter - you'll be fine as long as you catch the earliest flights as they have been 'parked' in CBR o/night. If you are relying on an inbound aircraft just be aware that you could experience long delays at certain times of the year.