Are there security precautions that need to be taken to protect visitors to my site?

A good host can't prevent you from most security attacks like others suggested. They can protect the infrastructure and their network but that won't stop someone from doing XSS or a MYSQL injection for example. Your coding standards matter. Security threats are bigger than ever. An SSL won't fully protect you either but you SHOULD have it. You will need to follow best practices for security when building a web application. There is many different types of attacks. There is lots of great information with examples on https://www.owasp.org/index.php/Main_Page .

when you sign up for everything (hosting, etc), they usually offer you a type of protection. the more protection the more money youll have to pay.

I think this all depends on the nature of the site. Is it an e-commerce site, or something that will be using sensitive user info? If so, you'll need to contact the hosting company as you will need a security certificate.