Good for you! I switched to English from western myself a couple of years ago, and I was in a similar "crash course" situation.
I would sign up for a couple of lessons with a trainer who has experience with English riding, with perhaps more of a dressage focus to start out since you don't plan on jumping right off. You won't need special tack for dressage or anything at your level, but that focus will give you a strong foundation. Most trainers will let you bring your own horse to ride, but if your horse is used to western, I would suggest taking a couple of lessons on a seasoned English horse, then bring your own and get some tips on the horse you will be using. The biggest difference I found was in the stirrups. It took some getting used to the shorter length and the "swingyness" lol. The secret is definitely putting that weight in your heels!
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown