Welcome to AFF, tysonius. There's a lengthy discussion on this very subject in
Flyertalk.
From that discussion, it seems several cards is the most beneficial arrangement - to take advantage of different offers, but unless you're putting a lot of spend through them, you need to watch the $25 fee for transferring to Krisflyer. ANZ Travel Card (1.4 KF miles/$ and 2.8 miles/$ on retail spend in AU/NZ) is quite popular. UOB also has a good card, I think 1.4 x on local spend and 2x on foreign spend).
Personally, I've stuck with the Citibank Premier Miles Card (1.2 mile/$ local + 2 miles/$ foreign spend ) which has the occasional bonus (3x foreign spend during long weekends last year, or 6 miles/$ for expedia spend at least through to 31 July). It also has a range of airline partners, most only have SQ and perhaps CXm but Citi PM as about 7 or 8 plus Hilton.
Most cards come with a priority pass (usually with 2 free entries per year) and some if you meet minimum spend threshold per month will give you a limousine voucher to the airport (and some cards it can also be from the airport). My partner has the ANZ travel card, which gives the voucher to or from the airport.
Very few cards have big sign on bonuses (in miles) like in Australia, but many have a renewal bonus (for example Citi PM has 10,000 miles for renewal - or annual fee waiver - you can't have both). Interestingly the annual fee waiver is automated, you dial in , "Press 2 for Fee Waiver" .... etc etc .
Good luck, but certainly have a look at the Wiki on the flyertalk thread I linked above, but bear in mind, there are some fanatics there, who have a suite of cards for every need, and seem to spend a lot of time chasing down every possible bonus point!