I play in the Cleveland HNA league. I was an absolute beginner last season, and into our 2nd season now.
Yes, teams are co-ed, yes there's no issue with women beginners.
The nice thing about HNA is that you all start together as a team going to 8 weeks of "Training Camp" where they help you work on your fundamentals, where to be on the ice etc. In Cleveland this training camp was run by Jock Callander, it was a little intimidating learning from someone with his name on the Stanley Cup, but Jock really spent a lot of time with each of us, helping us with everything from how to skate backwards to how to take a wrist shot.
As I mentioned, the best part is that you all start at the same time, you form a team that bonds really well. The worst part is that you all start at the same time. Meaning your team is facing off against the team that was new the previous year, and the team that was new 2 years ago etc. Every minute on the ice is invaluable and the longer you've played together as a team the better you are. As I mentioned it's my team's first full year, and we consider a "win" when we lose by less than 10 goals. It's something that every team told us would happen, and they've all gone through it. We see ourselves getting better with each game, and eventually will be closer to the skill levels of other teams.
Again, as far as women go, we had one lady on our beginning team at training camp, who played the scrimmages that first season with us. She was however the wife of another player on another team, and so after she had the basics of the game down, left to play with them. We have since added another woman to the team, who's a bit of a ringer, but we need all the help we can get
Rinks have always been accommodating, providing a separate changing room for the women. Most teams in our league have one if not more on the team.
Having played in HNA, and a summer league at a the local rink, I MUCH prefer HNA. It's a bit more expensive, and the fact that they keep all the stats encourages teams to run up the score a bit, but there is a level of professionalism, and sportsmanship that I didn't find in the house league. When we were absolute beginners fresh out of camp, and playing scrimmages against other teams, they'd help us out "Hey I'm wide open, somebody should be covering me!" Even now in our "regular" games there's guys that'll offer pointers after the handshake. When battling somebody in front of the net, I go down, and the first thing the opponent will ask is "are you OK?" We had a guy in our last game go into the boards awkwardly, the other team's bench cleared almost as fast as ours as we went to check if he was ok.
I've gone on and on a lot more than I thought I would, feel free to ask me any other questions.
One final suggestion, I took a lot of figure skating classes at my local rink and they helped me immensely, I recommend them to everyone starting out.