Regardless of which one you pick, will it work overseas with any local sim card from overseas? I do not see an option to just order the new iPad Mini Retina without a particular carrier.
Yes. But some carriers are less friendly about doling out new prepaid sim cards. TMob is probably the most generous, giving the out (online) for free from time to time.
Theoretically, yes. However, it's much easier to get a Sprint iPad and activate on T-Mobile than it is getting a T-Mobile iPad and activating on Sprint.