Firstly the best bet is to ring up a large gunstore in ur state who will know the laws back to front, even better than the police who can never remember themselves when u call to ask them.
Generally restrictions depends on what state. I think west australia might be more restrictive, but u should have no problem owning just five guns anywhere.
They may restrict in other ways-such as denying u too many of a similar type-say like 3 revolvers of the same calibre 'since u only need one'.
If the semi-auto 22 u r talking about is a rifle u will not be able to get it, unless under special circumstances-such as being a primary producer, professional culler used for destroying feral animals, or maybe being a collector.
Also u will have to check the barrel lengths on the handguns as there r heavy restrictions on barrel lengths under 4 ''
My opinion on ur selection is u have most things covered.
Good handguns, 22 for plinking & the kids to learn, lever action for short range pig shooting, & the 223 for longr range small game.
But techincally u still need a longer range big game gun.
something to take out pigs, deers, goats roos whatever to 250 yards or so.
The 357 runs out of steam on bigger game past 100 yards.
And the 223 rem while it has killed a lot of pigs is techncially still only a rabbit gun.On pigs & roos etc u have to really pick ur shots like neck or behind the ear shots.
If u want something to plant them with any decent centre body shot, or especially when running away from you('butt shot') the minimum to penetrate is the .243 & 6mm calibres & up from there.
A 243 is a good cheap choice & will reach out to a good range.
Of course u can go even larger with stuff like 6.5mm's, the various 270's, 308 is if u really want & up from there.