For a lot of games (RPGs in particular) it depends on how much I enjoy the gameplay systems. If I'm not a fan of a lot of the gameplay aspects, I'll just stick to what works.

In shooters I tend to try out all the weapons, but I do gravitate towards the slower, hard-hitting accurate weapons (snipers, revolvers etc), I'm a "headshot from a distance" kind of guy.

In games that offer stealth, I stubbornly stick to stealth as much as possible. Uncharted games I stealth kill as many enemies as I can before the inevitable shootout. Dishonored/Deus Ex and such, I 100% stealth all the way, saving/reloading frequently. Far Cry, Tomb Raider and other shooters with silenced weapons, I always use silenced weapons to pick enemies off one by one.