When Q showed up on the Enterprise-D, generally chaos ensued with a few notable exceptions. By the time of DS9, standard Starfleet policy regarding Q probably was that the best way to deal with him was to ignore him, not play into his games, and hope that he gets bored and goes away...I found it funny how Sisko and Janeway reacted when Q came around. Alland acting like he was an annoyance.
For Picard it was OK as he's dealt with him a few times, but they looked a little silly saying "What do you want Q? We don't want to play games!"
If I was a Captain and I got to meet him I'd be acting like I met a celebrity.