I usually play through a game once without worrying about scores, and then after I'm done I check out the trophy list to see if getting a platinum is feasible. Some games are (it looks like Battlefield 4 is an attainable platinum and I might go for it) while other games are not (the online trophies for Assassins Creed 4 seem far out of reach)
Platinums: Red Dead Redemption, Killzone 2, LittleBigPlanet, Terminator Salvation, Uncharted 1, inFamous Second Son, Rocket League