I am always the most fun rper (and having the most fun) when I am a big fan of the characters of the people I am playing with. The things mentioned above about showing interest in my RP partner’s character and considering their hooks and everything is a lot easier when I am sidling up to them and metaphorically twirling my hair around my finger as I go ‘hey I think you’re cool want to rp after work today?’
To that effect, I actually start a lot of my efforts to be a good rp partner with how I build my character, because I want to be someone those cool characters might have a fun time with.
What are my character’s goals, and what things will they be unable to accomplish on their own? What ways can I make them reliant on the expertise of others?
What themes in the setting allow for shared elements of history, worldview, and trauma, that will give my character a chance to build meaningful relationships with others?
What traits will draw my character towards someone? What will push them away? How do I balance the character so that levels of interpersonal friction remain fun? How do I make it so I am not fighting my character to set up RP? (i.e. how do I find workarounds for the they wouldn’t go there/do that/talk to them shutdowns that might happen on my end.)
Most of this isn’t a formal checklist, but I know I’ve done a good job of it when I’m looking at other characters pages and going ‘oh it would be fun to have my character do x with them.’