Welcome to the forums and good luck with the new campaign.
1) Be liberal with Conviction, both encouraging it's use and in using it as a reward for doing well. Whether that's roleplaying well, being creative and exciting, having their characters do cool stuff (leaping off a wall to impale one orc while hurling a burning flask of oil into the barracks entrance), working up a good plan, or for taking a string of bad dice luck in stride ("Geeze! That's your fourth 4 in a row. Have a point of Conviction.").
1a) Just remember that they have a limit of Conviction. For great RP before they've started spending it, you can make notes for awarding Conviction later in the session.
2) In your GM notes, make sure to include the usual numbers (defense, Notice bonus, Stealth bonus) and their character Natures so that you can reward good roleplaying. Nature is just a tool to reinforce RP, so your players shouldn't have any trouble following it; you just need to make sure you notice in plenty of time to reward them with Conviction.
3) Use the Minion rules. Minions are a great tool, since they can be very capable without being long-lived. Bonus, they vastly decrease the GMs bookkeeping.
4) Don't be afraid to remind them that the world is a dangerous place. Ambushes are very deadly, and even a lowly crossbow can drop epic heroes. This works in their favor as much as it is a danger for them.
5) Be willing to have enemies do non-lethal damage for a fight or two. It's just as difficult to resist as lethal, while not having the character removal of lethal. This is mostly so that you and your players can get a better sense of just how durable their characters are without the unfortunate need for PC generation.
6) Most of all, keep it fun. You have a pretty good idea what your players enjoy, so keep the game in that style. Make it challenging, but keep it in the style they enjoy. That's the best way to make them want to do it all again.