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Tips: Buy ammo for the first unlocked gun. It's accuracy is decent and damage is good.
The shotgun is only useful when you haven't unlocked the sniper-looking thingy. For clean shots on the guys with armour everywhere but the stomach. The 1st unlockable gun (pistol thingy) is good for anything else.
The red dot (aiming thingy) stays the same place if you switch from an accurate weapon to a less acuurate weapon. This can be used as an advantage, like switching from the sniper and then to the shotgun and firing quickly.
Save most of your souls for the machine gun, about 150 in the pistol and 70 in the sniper should be enough for any level. (I think.) Once you get the machine gun unlocked, use all your sould you gain to buy it. It's acuuracy is the same as the original revolver you start off with, but with the sniper you can easily fix that. If you're having trouble switching weapons, think of the red dot as the aiming rather than the grey circle. The grey circle is the area the red dot will move around in as well.

Gaining extra points:

Clean Shot - Kill someone in 1 hit (100 Points)
-Most important thing for gaining points. Killing in a few shots will only give you souls really
Long Range Clean Shot - Killing someone while they're far away in one hit . (200 Points???)
-Was too hard for me to get 5 in a row. I don't reccomend it.
5 Clean shots in a row - Self explanitory (??? Points)
If you keep raking in the clean shots, bonus points!

That's my wall of text. Now go out there and shoot some headshots!