Shield tanking
Level 1 = w/e
Level 2 = Caracal passive tank
level 3 = Drake passive tank
Level 4 = Raven active shield tank or passive shield tank nighthawk ( raven is better )
All of which are awesome suggestions for a Minmatar pilot.....
Level1 = Rifter one of the best small ships in the game, fast, good capability and cheap to lose. Speed tank (you rely on being fast and hard to hit rather than tanking the damage)
Level 2 = Rupture, armour tank or Stabber, shield tank
Level 3 = Hurricane, armour tank or Cyclone, shield tank
Level 4 = Tempest, can be tanked with either or Maelstrom, shield tank.
Those are my suggestions for suitable mission-running ships.
For level 4 missions the most popular ships are the Dominix (Gallente, drones and armour tank) or the Raven (Caldari, missiles and shield tank). That doesn't mean that Amarr or Minnie ships are bad for mission running, just that they aren't as popular.