Before the start of each mission, you'll have the option to choose which weapons you want to use for it. Some missions require something with power, like if you're taking on helicopters or tougher enemies, and sometimes an assault rifle like the Vz.83 Skorpion will come recommended by the gunsmith.
Assault rifles are pretty much the way to go. Pistols are good for accuracy, but have a poor firing rate, shotguns are good for power, but don't have the same level of distance as assault rifles. RPG's are nice, especially when it comes to blowing up cars, but they take a while to reload.
If you can, stick with higher grade assault rifles, and you'll have no problem moving on in battle.