2nd turn: Easy, Hard. Hard missions can give you some cool stuff, but I feel the only real good time to do them is early in the game. This is the earliest you can.
You can fulfill a hard mission in turn 1.
Get the stuff for your medium mission, and two crowns. Do your medium mission, draw a hard one, fulfill it with your crown chits.
(with one crown and 1-2 spare other chts you have a chance to fulfil the hard mission, but it's not sure)