If the library site serves over plain http, it is fairly easy to snoop on the visitors activity. So one could find out which kind of books certain visitors were

If the library site serves over plain http, it is fairly easy to snoop on the visitors activity. So one could find out which kind of books certain visitors were looking for. That could easily reveal secrets about said visitors. If we are not just being hypothetical, a simple solution for you could be to register with cloudflare and run your site behind that. They will give you a free ssl certificate. This isn't as secure as running your own, since the connection between cloudflare and your server is in plain http, but it's a lot better. As an added bonus, you get a free caching layer in front of your site, which might be a good thing if you're on a small shared host.