Co-writing is like dating in so many ways. You're looking for someone who inspires you. You're looking for someone who can make difficult work fun, someone who can help make the future look bright even though the road ahead seems so unclear. And you're looking for someone who can tell the truth - as well as recognize it to begin with.
Of course those dates will cost you something - at least half your profits, if not more (should you wind up on a date with several people at once).
Nashville's unwritten rule is, "if you're drinking coffee in the same room as the writers, you get an equal share." Wow, is that fair?! Yep, especially if you co-write over a period of many years. Things have a way of evening out. And there is so much less haggling to do! But maybe you like haggling...
During my years in Nashville, I wrote with many people, but mostly with just one guy. Greg was from New York, a converted jew and a talented idea man. He could come up with a verse for almost any topic - quickly. But he needed help fleshing it out. And using the word "whore" at least once in every song was not an acceptable practice. We made a good team - at least in terms of how well we got along, our goals with the songs and our level of writing. We didn't actually get any cuts (although I won't be surprised if we land a couple eventually), but we worked well together. Part of the equation is whether or not you can crank out something that you feel good about. The other part is whether or not you can have a good time doing it. That sounds like a good date to me.
A different writing partner was really good at not sweating the small stuff. Sweating the small stuff bogs you down and kills the process. I realized after writing with him a few times that he could recognize when something was unimportant and let it go if the problem it created couldn't be resolved quickly. There would be time for rewrites later.
And finally, to reiterate, a good co-writer is someone who can tell you the truth - and hopefully do it with some modicum of tact. But truth trumps tact. This is a tough business. If you have a hard time with people who are direct, you might...gee, what is a profession where the best practitioners are not direct? I can't think of any.