Don't bother buying the cheaper guns, as they aren't any better than your starting pistols - save up your cash and buy the beefy weapons, instead.
Weapons you own are upgraded using the coin currency you loot from zombie corpses. You'll need to head into the shop and then select the Upgrade option to increase damage, ammo size and firing rates.
When you're asked to protect a target, a good tactic is to simply run back and forth past the target, as your hero will then automatically kill anything that is near the target.
You won't be able to make progress through the game unless you've successfully completed enough of the reels. To top up your total, head back into earlier levels and try to master some of the objectives. This will help you get ahead, and earn you some precious currency and XP.