Need a Booking System for a Horseback Riding Stable

Our riding club runs lessons for both complete beginners and experienced riders, and right now all scheduling happens through phone calls and a paper board in the stable office. It works, barely, but we keep double-booking horses and forgetting that an animal that just finished a lesson needs real rest before going out again. I want to move this online and I'm looking for someone who has built booking or scheduling tools before, ideally for sports clubs or anything with limited slots and recovery time between them.

The core idea is simple from the client's side: a rider opens the booking page, picks their level, novice or experienced, optionally requests a specific horse they have ridden before, and chooses an available instructor and time. Behind the scenes the system needs to check how long since the horse's last session and only show slots where a suitable horse and instructor are both genuinely free. Novices should only be matched with horses marked calm enough for beginners.

I would like an admin panel where staff can override matches, block a horse for the day for a vet visit or bad weather, and see the week's schedule of horses, instructors and riders at a glance.

Please share in your proposal:
— similar scheduling projects you have built
— how you would handle the horse rest-time logic
— a rough timeline and price