Hi, I have gone through your requirement and as per my understanding you are looking for a web expert, who can help you to build a beauty salon website with online booking functionality, yes Paypal or stripe (both are can be integrated in your website, but I will recommend PayPal will be best for this website, make your website mobile friendly as well, so this website will support all type of mobile like, iPhone, Ios, I pad, Tab, many more. I would like to provide you a free mock-up design for this task, provide you with unlimited revisions as well, I do have queries like: will you provide us with the logo and content? your contact details should be easily available on the top of the website, we can add a button like "Book an appointment" for quick contact, There need to add Testimonial page where you can show positive feedback from your client, which help you to increase the conversation rate,
NOTE: SEO part can be started from the designing phase, let's connect so can discuss with you more regarding this task and I can suggest you better.
Regards
Dipak