Willowtigger, I used to teach people to ride. If you can only take one lesson a month go for it. Once a month is better than not at all. As others pointed out, it will take longer, but better than nothing.
Some points to consider when choosing where to go. Some instructors don't want to accept students who are not planning to show. Personally, I was willing to teach anyone. I appreciate that not everyone wants to compete. I appreciated that some just wanted to enjoy being around horses.
Check out the teaching style of the instructor of the other barn. Make sure their style and your personality are a good fit.
I can't tell you which barn/instructor to pick, but I would suggest you go with the place you are most comfortable with.
Welcome to the horse world. It can be a wonderful place!