Dead Rising is full of beginner traps. Get used to it, on your first go the game will have a good time kicking your ass, and you will come back for more the second time around. Don't be afraid to run to make your deadlines, aside from the main quest there is nothing you really need to do, it's all optional stuff and it's better done on the next playthru when you're leveled up and more prepared.
Cletus gives you access to the gun store, which lets you get two shotguns and two sniper rifles(they don't respawn until you drop them or use them up). This is entirely optional as I rarely ever kill him and do just fine, do be aware that he does go away on day three so you can get his guns anyways. In fact, there is a hidden scoop there with three survivors to rescue, just be sure to photograph(and lock in the photos menu) the vent in advance
BTW, just like someone else above said, there is hidden Submachine guns all over the mall, one in each area, these should be doing bulk of your ranged damage. There is one on top of the rooftops in Paradise Plaza, you jump up from the stairway to the roof above the kids clothing store, another one is in the underground tunnels where the key to locked doors all over the mall is, there is one in the Food Court on the top of the sign within the Italian Restaurant(one with the plates, right next to the cartoon chef) and one in the fountain in Al Fresca Plaza. There is more, but they're too hard to get so I never bother. Just like shotguns/sniper rifles they don't respawn until they're used up so you can't farm them.