Do I need to make my entire website secure?

Hello, I have purchased a secure certificate for my website and if I go to https://www.mydomain.com everything is working fine, however when I just type in mydomain.com it takes me to the unsecure http://. I have found a few plugins that force https but is this really what I want? Are there any downsides to forcing a secure connection on every page of my website, or should I just force a secure connection on checkout pages/forms?

I also read somewhere that instead of a plugin, I can just change my “WordPress Address” and “Site Address” in the general settings to https://… is this correct?

Thanks for the help,
Zach