In my experience, the most successful gigs are fun - generally because most of the top choices get checked off. But THE thing that has made gigs fun for me is an attentive appreciative crowd. I'm not at a level where the money is much to be worried about; the paycheck basically covers my expenses for the night - most of the time.
I've played a couple of gigs where I commented to a band mate that I would have played THIS for free. I've also had the gigs where none cared you were there (same band, same venue) and there just isn't enough money to compensate for playing that last set to the three soon-to-be passed out drunks at the bar.
Yeah, I guess getting invited back is pretty important, but I didn't vote for that because, if the things I did check off occur, we're probably getting invited back, so that's more of a dividend of a successful gig rather than the definition of one - IMO. I've been in bands that got invited back after gigs that were not otherwise successful, and not after ones that were.