Do you mind if I ask what area you are in?
My first thing I suggest to new riders is research. Look for reviews on the stable. Go and just take a tour and notice little things like the condition of the horses. Are they healthy weight? Do they look happy and content? Does the barn look safe? As in no nails sticking out, things for horses to get caught up in. Does the hay look good quality?(even take a sniff and make sure its not moldy hay) Is the barn clean? Well maintained? Sit and watch a lesson and listen to the coach to see if her/his teaching style would work with you. And last but not least, certification. Coaching certification is huge. You wouldn't send your kid to swimming lessons with an instructor that isn't a certified life guard would you?
The other thing. What sort of English riding are you interested in? Are you looking to get into dressage? Jumping? Pleasure riding? Do you want to show?
Put together a list of questions for the coach. Ask their certification. Ask when they last updated their first aid course. How they advance students. How do they start students out. Do they teach theory and equine first aid, including stable management. Ask how many times a horse will go out in one day for a lesson.
The reason I say look at simple things like the quality of hay, how clean the barn is and how many times a horse goes out a day for lessons is because things like this speak volumes on the facility and pride they take. Are they mass production or do they actually want their students to learn and learn to ride safely? Also the care of the horse says if they actually are in it for the horses and students or are they in it for the money.
You are learning to ride a 1000lbs animal that has a mind of its own. You want to learn somewhere that values safety and the care of the animal.
Any questions feel free to ask away
And welcome to the addicting world of horses!