I play always to my character; for instance, on console, my second character was a slightly psychotic ex-NCR Ranger, so I played a hardline NCR playthrough and outright slaughtered anyone who even slightly disagreed with their ideals.
This playthrough, I'm playing a character who I'm writing a Fallout fic for -
Null, a former Enclave child soldier-turned-courier (Vault 101 start be damned!) with some serious anarchist tendencies. Basically, he'll recruit everyone he can, use them, and once they're spent, discard them - all in pursuit of bringing down what he sees as a failed world (he sees the Legion, House and NCR all as representatives of that world).
Thusly, he's a pretty hardline Independent player. The only groups whom he has any sympathy towards are the small communities; they remind him of someone he lost in the distant past, and he views these tiny communities like children - innocent, without sin. Thus, he will fight to protect them, but if they should happen to hamper his goals, he'll cut them down like the rest.
It's a fascinating playthrough, let me tell you :)