I usually just grab some of the ones that come through a normal play-through. But I also tend to gander at the trophy list so there are times when I'll try to nab certain obscure ones when the opportunity arises just to spice things up. For instance, I kept failing and re-trying a certain boss fight in Batman: AA so I could get the silver trophy for winning with a prohibitive tactic (take down a Titan without a batarang). It's one of those ones that seems like it was thrown in to pad out the trophy list, but it actually ended up making me a better player by forcing me to use tactics I wouldn't normally use. My repertoire was deadly from then on out.

As for completing a trophy list, I don't have a single PSN Platinum yet, although I'm pretty close on a few (Batman: AA and Bayonetta) and getting up there with a couple others too (Fallout 3, SSF4). I also have 100% on a few downloadable titles like Flower, echochrome, and PJ Shooter, but none of those offer Platinums.