You don't need to install mods, the games can be enjoyed vanilla. In my experience, I've found Clear Sky to be more stable than Shadow of Chernobyl, insofar as it doesn't randomly freeze when loading a saved game. However, the faction war quests can get bugged, as well as the end-game on rare occasions. Call of Pripyat is the most polished one. Other than that, the games run fine, and I don't think I've ever had a crash-to-desktop. I've played them on Windows 8/8.1 though, who knows if that affects stability.
You just have to ensure that you save your game a lot using different save-games, and taking the time to manually save the game instead of spamming the quick-save button is well worth the trouble.
Three pages in this thread and people are still wondering how exactly the shooting works in these games. Well, here's the thing - you must play at the highest difficulty, doing so means that both you and the human enemies would die in <= 3 shots on the torso from any gun if you're unarmored. The way the guns work is that bullets generally travel in a straight line, except that after every shot, the crosshair is randomized ever so slightly, and the extent of this would depend on your stance, movement and the type of weapon that you're using. There is an effective range of bullets depending on the type, and it is recommended that you use semi-auto for most of the encounters. Keeping all these things in mind, you can clear out multiple human enemies with low-quality armor in close-quarters combat equipped only with a good handgun if you know what you're doing.