WordPress Booking Plugin – Seaside Holiday Website

I'm looking for an experienced WordPress developer to build an online booking system for a seaside holiday property website.
What I need:

A calendar-based availability and booking system, where guests can select their desired dates
Payment taken directly on the website via Stripe
Once a booking is confirmed and payment is successful, the calendar should update automatically to show those dates as unavailable (ideally visually distinct — e.g. dates shown in red or blocked out)
The solution should be clean, user-friendly, and mobile-responsive

Tech stack: WordPress (existing site)
Budget: I'm working with a limited budget, so please keep this in mind — I'm open to plugin-based solutions as well as custom builds, as long as the end result is reliable and professional.
What I'd like in your proposal:

Your suggested approach (plugin or custom)
A clear price for the work
Any examples of similar booking systems you've built previously
Estimated turnaround time