Coupla hints I found useful
Search the bodies of every kill you make.
Search the caches as they are revealed - some contain some real treats.
Carry more than one calibre of weapon - In the early stages I had 5.45mm [Soviet] and 9MM [crappy sub gun]. In the later stages 5.56mm and 9mm [Duty assault rifle]
Do missions for both Duty and Freedom - the reward is often AP rounds.
When you've completed said missions, kill everything in sight - the Duty and Freedom characters carry good weapons.
Go backwards and forwards through the Wild Territory from the Bar to the Scientist lots of times. Killing Mercs is a great way to harvest 5.56 rounds and the scientist trader sells 9mm and 5.56mm.
Doing those things meant that I went on to Pripyat carrying almost 2000 rounds and still collected almost as many as I fired from the bodies of my kills.