I was transferred to Melbourne from Sydney with work.
No problems at all finding accommodation. The public transport isn't too bad, although I try not to use it if I don't have to.
Personally, I think your better off living somewhere closer to the CBD rather than near the airport. St Kilda (East and West are both nice and less expensive than St Kilda proper). Windsor, Prahran, Malvern, South Yarra are also very nice - a little more expensive but its only a 20 min drive to the airport. Carlton, Fitzroy, Collingwood are also fairly central and again only about a 20 min run to the airport.
There's lots of share houses around and you should probably have a look at
www.heraldsun.com.au or
www.theage.com.au for share houses. Or use the find a flat mate sites that exist in their thousands!
PM me for more info....