Dead Rising Newbie Questions

So I've had Dead Rising for a couple years now but for whatever reason I've just never finished it.  But my wife LOVES to watch me play, so I installed it last night and started whipping some zombies.

But I realized after I was done and I let Jeff and Natalie die that maybe that wasn't the best use of my time.  My thought is to level up as quickly as possible to make the game's difficulty a bit more manageable.  I definitely had problems in some of the day 2 missions with how hard the game got and I think if I leveled up my character a bunch and then went into "new game plus" mode that it would be a bit easier.

So what's the most efficient way to level up?