Yes exactly, https website is now become almost mandatory. You should go with hosting assured companies who follow primary security standards.
You can go with either free or paid SSL certificate providers. Some of the top hosting assured webhosts are:
- NodeSpace Hosting
- Blogvisa Hosting
You can check the hosting assured webhosts here.
As said above, if a hosting company provides cPanel, then it surely has a free SSL Certificate for your website. They are from AutoSSL but powered by COMODO - a trusted SSL provider. If you are looking for cheap website hosting with free SSL included, be sure to checkout THCServers.com
If you have a private server then you can get a free SSL using let's encrypt which is a technology which even we use to offer free SSL certificates with affordable hosting.