I’d like to recommend Carrd as the website builder. It’s super easy to use (seriously easy). It is crazy cheap ($9/Yr) and has a free tier for you to try it before you do commit.
For the scheduling part there are a couple of different tools for you to choose from that I can currently think of.
These can be embedded into your site with a simple copy/paste code. They are called;
Goodluck, let me know how you get on.