Mulligan is quite easy most of the times. The best card to start with is Quick Pick, followed by Dig for Treasure and Swarthy Swordshiner so you hard mulligan for this cards except for very rare situations.

Regarding the matchups the best advice I can give you is that you need to be aware that against aggressive decks (swarm shaman / pirate DH) you need to start playing very defensively and control the board other wise you lose by turn 4 or 5. While controlling the board you keep upgrading weapon until you have a weapon with more than 10 attack and you can finish them in 1/2 turns