This is really the thing that's going to add some spice to the roleplay; when characters disagree about how to approach a situation and have to talk it out, or whatever the outcome is.Also wouldn't it be good to have non-chaotic goods on the team too? My character will be chaotic neutral but surely a lot of fun would come from how different character types want to approach different situations, right?
I'd guess if we're approaching it with everyone loitering around the the tavern waiting for a quest to come up, you can decide if it's something your character would participate in or not. If there's a party with 4 chaotic evil players already in it, the lawful good paladin might just choose to sit it out.
But a mix of alignments would be best, for sure.