I stopped the lessons at my old barn and took a break to find a new one. When I did at my first lesson I asked a LOT of questions. Like "how is this horse at doing this?", "who's this?", "do they bite?" And since I just switched to English I also asked stuff about the tack. It was a fun process, I love my new barn and the horses! Make sure to ask a lot about the horses (to see what horses you may want to avoid or have more predation with), where stuff is, and how the barn usually is.
You definitely need to consider all your options before moving. Look at a couple other barns and compare to your current. If you do decide to leave try and leave on good terms so if you need to go back you can. The trick is to just keep all your options open