If you have an iMac G5 it would not be from 2012. Anything newer than 2006 would
likely be Intel-based. To upgrade an OS X past the native version requires a retail
OS X install DVD; a purchase. So it helps to know what you have, as the limits are
published. (I've had trouble posting here, second try.) G3/G4/G5 are PowerPC.
If both of your recently acquired Mac computers are older hardware that pre-date
the arrival of Intel processor technology, they are unable to run an OS X newer
than Mac OS X 10.5.8, if they have a processor speed of 867MHz or better. For
those with slower than that, they'd be stuck with OS X 10.4.11. Or older OS X.
To correctly identify the hardware build version of each product, the Mini and iMac
would be essential to knowing what you have and then making a suggestion.
Upgrades to system software and applications to run on the newer, are limited by
the hardware build model of the computer; so that is key to how to purpose these.
Sites such as Everymac.com can be viewed with an idea of matching your model
products by specification, and that can tell you some detail plus expectations.
Also a fair download database for most things Apple is available from MacTracker
See http://mactracker.ca for details on what it is, & other info.
The PowerPC architecture has been vintage or obsolete, with limited to zero support
for some time now; however the products can still be used for a variety of projects
if you have software for their vintage. There also are browsers such as TenFourFox,
SeaMonkey for PPC, and iCab, among a few others that do well in pre-Intel Macs.
The Intel-based Macs have their own limits going forward... from 2006. Several do
not fare so well in the Early editions, past Snow Leopard 10.6.8 or Lion 10.7.5. To
upgrade past Snow Leopard, for those supporting that, the Mac App Store is needed.
You can buy Snow Leopard 10.6 on DVD from Apple. Update it free online to 10.6.8.
But it won't work on PowerPC based older Macs.
Good luck & happy computing! 🙂