What I would want is probably very different from what a new homeschooler would want, if that makes sense. I've been homeschooling for 13 years, so I'm looking for companionship from other moms and events where my kids can just .. hang out.
So I have no interest in co-ops, although my boys do take art classes in our local homeschool co-op, simply because they're taught by a professional artist and I draw stick figures. :D
We don't do field trips either, unless it's something really special or extraordinary (for instance, our homeschool group was able to organize a field trip to the FBI Academy, which isn't open to the public. That sort of opportunity is what I would be looking for as far as field trips go. If we can just go somewhere as a family, we prefer to do that.)
The group I belonged to when we lived in Maryland had a Mom's Night Out, which was awesome!!! Once a month, the moms (and we had a few dads, too!) would get together at a local restaurant and eat appetizers and desserts and just talk. We tried to meet some place that wasn't crowded, so we didn't feel that we were rushed, and where the food was relatively inexpensive, so that all moms (and dads) could come and enjoy the evening without spending a fortune. We often wound up at Denny's because they're always open and you could have an entire meal with endless cups of coffee for under $10.
I would want a group that is open to all homeschoolers, no matter their religion or lack thereof, but that's what *I* would be looking for. I wouldn't join a homeschool group with a statement of faith or anything of that nature...and never have.