Now atp-get tells me there are 16 updates available and the Mint Update icon says there 3 updates. Should I install both or just the Mint updates?
Definitely not the apt-get ones - there are updates to the kernel and ATI drivers (fglrx) I have ATI now so I've sen it
There's a high risk your success with graphics changes into failure...
This is why we recommend mintUpdate - it sorts updates so that potentially dangerous ones are not shown (even if it has a bit of a problem finding updates in older versions)