You need Duranium, Corbomite, Boronide, Mercassium, Uridium, and Gallicite to build a geosurvey ship. (Technically you could put off the Corbomite until you build a cargo ship if you use survey fighters, but you still need it eventually.)
And Sorium to fuel it of course.
You need Neutronium to build shipyards.
Corundium to build mines.
Vendarite to build a cargo shuttle bay so that your cargo ship can interact with your offworld resource locations. (Maybe you could skip this if orbital mining goes directly to cargo bays?)
I think you could get off your homeworld without any Tritanium. Any other TN mineral missing and you're going nowhere, barring non-modeled conventional alternate techs for pre-TN extraplanetary resource recovery.