The licence required for an aircraft type is dependent on the class of operation ie Private, Aerial Work, Charter or RPT and, when the type is a multi-pilot type used in non-private ops, the pilot's role in the aircraft ie PIC or CP. The <5700kg limitation is the Single Engine <5700kg group endorsement all of us probably have on our PPL, CPL &/or ATPLs.
In Oz there are some PVT category operations that allow a PPL to be paid. Payment received by the pilot only has an effect in so far as it affects the class of operation, otherwise it is irrelevant. s
A PPL can be PIC of other aircraft types but, just like the SE<5700kg endorsement, the pilot must hold an endorsement for that type that authorises PIC - so a co-pilot endorsement isn't sufficient. Unless there is a specific restriction on aircraft size or capacity then there is no limit for a PPL holder eg share costing rules only apply for up to 6 (seats available, or POB for that flight? Can't remember). But if the PPL holder pays for the flight then the share cost rules aren't applicable.