Level-up each hero's basic attacks first (they're the two on the left), as these are the most common ways to fend off attackers.
Later powers, such as bombs, are more devastating but take longer to recharge.
Every attack has a cooldown period before it can be used again, and hammering it won't make it work any faster. We tried.
Watch out for mega-expensive potions on sale mid-battle. They're easy to buy in the thick of battle with a careless tap, and could wipe out your virtual finances.