When playing as Rafaam, you should buy a minion and Hero Power on turn two instead of upgrading your Tavern. You may even want to delay your first Tavern upgrade all the way to turn four and follow it up with rapid upgrades on the following turns. Keep an eye on your opponent though! A.F.Kay and Ambassador Faelin have no minions on turn two, so you cannot steal anything, and some powerful early-game Heroes may have too much power on the board for you to kill anything, in which case you also do not get a free minion.
If you have activated your hero power, but you do not kill a minion in combat (due to the enemy not having any, for example) you will still get a compensation Gold coin.