Let’s Encrypt will work fine for that purpose. You would not need to enable Full SSL (strict) but you would be able to, and this would improve the security of your site. This applies whether you use a certificate from Let’s Encrypt or CloudFlare’s Origin CA (mentioned later).
However, you should be aware that Let’s Encrypt certificates expire every three months, and you have to go to sslforfree.com to get a new one. If you forget, your site could be inaccessible until you do. For that reason, most of us prefer to use web hosts that support Let’s Encrypt natively or give us the ability to install software on our servers that renews our certificates automatically.
If you are using CloudFlare and a web host that does not support Let’s Encrypt or root access, you will be much happier using CloudFlare’s Origin CA instead:
If you don't know of a reason to prefer the Let's Encrypt certificate, the CloudFlare Origin CA is preferable for this purpose. Note that if you ever stop using CloudFlare, you will then have to obtain a different certificate at that time.