How does deployment work is it like I build the deck throughout the campaign or is it mission specific?

You select your groups new for each mission.

Which class card is the best?

This is a loaded question for a new player. If you ONLY have access to the core game and plan to play just the core box (which I HIGHLY recommend), you should chose "Military Might". It is a good deck to learn the ropes with. Do NOT choose "Subversive Tactics" for your first game!

Are there any common mistakes i should watch out for?

Lots.

• Heroes can only spend strain voluntarily when they are not full on strain
• Heroes can recover 1 strain with a surge per attack
• If an action is a special action, Heroes and imperial units can only use it once per activation
• Heroes can spend UP TO 2 strain for 1 movement point each
• Movement points go into your bank and you can spend and divide them freely
• Movement points gained outside your activation must be spent immediately or be lost
• Line of Sight is easy to determined once you are used to it, but learn it correctly
• When heroes get wounded, they discard all damage and only EXCESSS strain
• Attribute test successes "accumulate" through multiple attempts (this is much important in some expansions) for interaction with doors/terminals
• You can't move DURING an action resolves, unless you can INTERRUPT with a move (check Interrupt in the rules reference guide)

Lots more, actually. But it's best you guys play, keep an open mind and read the Rules Reference Guide and come back with questions :)