iPad mini 3 bought from United States I bought a brand new iPad mini 3 64GB from a auction site, I knew it was imported from the US, that's fine, I'm now unsure as to what SIM card I can use in it, it won't accept an O2 SIM card.

Can I use it in the UK on cellular, if so what network SIM card might I have to get.
No iPads have ever been network locked and all current model iPads with cellular connectivity support both CDMA and GSM networks (see Apple's LTE information), with no frequency limitations.

What that means is that your US-purchased iPad Mini should work just fine with an O2 data SIM (and any other UK data SIM for that matter - EE, Vodafone or Three). If your SIM isn't working, I'd verify:


Is it a data SIM? 
Does the SIM work in other devices (eg, try in a cellular dongle)