Online booking system for my hair salon (web + simple admin)

I run a salon with 6 stylists and we book everything over Instagram DMs and a paper diary — it's chaos and we lose appointments. I need a clean booking page where clients pick a stylist, service, and time slot, get a confirmation email/text, and can cancel or reschedule themselves. Admin side: a weekly calendar per stylist, block-out times for breaks, and a simple client list with visit history. We use Square for payments so deposits would be great but can be phase 2. Mobile-friendly is a must, most clients will book from their phones.