The Comedian is portrayed as a cynical, nihilistic, and sadistic thug, using unnecessary violence and even committing crimes himself, like his attempted rape of the original Silk Spectre and his murder of his Vietnamese lover.
Once employed by the government, he is heavily implied to have been the assassin of JFK.
Given all that, what was his motivation for joining the Minutemen as a crime fighter?
I believe a bit of questioning the premise of the question is in order here: did he really want to become a crimefighter? According to Before Watchmen: Minutemen he was hardly more than a thug before he joined the Minutemen:
There's also the bit from Watchmen #4 ("Watchmaker"), where Jon recounts his experience in Vietnam with Blake:
In addition to a thug, he was also a sadistic maniac. One can imagine a scenario where he starts as a guy beating up people who just happen to be some kind of baddies. He then goes on to join the Minutemen, probably because the job description fitted his tastes, and maybe also because that would place him on the right side of the law, and get him a bit of money.
Next the Minutemen disband, and he goes on doing government's dirty work (basicaly same thing he used to do). He sort of continues to do crimefighting, as seen in the scene where he and Night Owl II address a protest. There we see his attitude towards the "American Dream", which also demonstrates his broader philosophy (nicely outlined in detailed answers here).
I find some modicum of explanation in the watchmen when comedian shoots the pregnant woman while dr. manhattan stands and watches. The comedian then rails at dr. manhattan that he could have stopped the woman from dying with a single thought yet hadn't. The comedian perceived reality at a level where he saw only 2 options; laugh at it all or cry. He wasn't the crying type.
