For the tank-type missions:
- To get the Object 260 you obviously need a Tier VII arty.
For the country-type missions:
- You need an Alliance and Union arty to do the primary missions for the Excalibur (need Tier VI) and Chimera (need Tier VII).
- You need both a Bloc and a Coalition arty to do the secondary missions for the Excalibur line (need Tier VI, but this is for the secondary missions, which you don't need to complete for the vehicle).
- There are no arty missions for the Object 279 (e), which require Tier VIII vehicles.
So to obtain all the mission vehicles, you need a Tier VII Alliance and a Tier VII Union arty, and you can just buy a Tier VII Russian arty from the collection vehicles (you don't need to research one). For the Alliance arty, the American Tier VII has one of the highest Stun Per Minutes of all the Alliance arty and should be more than enough to complete the missions.