I would like to use Let's Encrypt for automated encryption, but as GoDaddy doesn't support this, I would like to know the best hosting company to move my websites to. Free is good, but reasonably priced with good security and SEO is important also.
Really, it's totally up to you. I would recommend a VPS with shell access, and your provider is up to you, AWS, Azure, Vultr, DigitalOcean, whatever. They all have different featuresets and prices, all of which are up to you to decide.
Generally, shared hosting providers limit your usage of other SSL/TLS methods because they are paid from companies like Sectigo or VeriSign to do so, where using a VPS/VM with shell access almost always has complete access to Let's Encrypt.
There's a community list of hosting providers that work with Let's Encrypt, though it doesn't give much information about why to choose one over another,
I know some people have managed to integrate Let's Encrypt with GoDaddy despite them not making it particularly easy themselves. (@griffin, here may be another test user for you?)
I developed the CertSage ACME client specifically to help GoDaddy shared hosting users who use cPanel and don't have root access. It's not totally automated to acquire certificates, but for only entering an email address, typing in your domain, typing any subdomain names, and pushing a button on a webpage, it's very quick and painless to use. You just need to copy and paste the certificate and private key into cPanel from there (though soon I'll release an update that automatically installs those into cPanel for you). The entire installation process of the client consists of downloading one text file, uploading it to the public_html folder of your hosting account, and changing the extension from txt to php. I've had quite a few satisfied users with the beta version thus far. If you want to try it out, I can send you the step-by-step instructions. It's free, of course.
I shoved a SSD in a decade old Lenovo X230 and installed Linux. More CPU cores and more storage than any cloud vendor offers and the cost of operation is negligible with low electric rates.
I set my machine up to handle multiple websites should my developer services be required. COVID has hampered me to help some small businesses develop a web presence.
certbot is free and it can handle as many sites as you want, as long as you not renewing 4000 sites all at once etc
Technically, you can also just move your DNS over to another provider like Cloudflare, Akamai, Verizon, or AWS, many of which allow reverse-proxying to make getting SSL certs even easier, while maybe not coming from LE
I did PM @netrasusan the package for the CertSage Beta Test, but haven't heard back yet. So far of everyone who has tried CertSage, they've been more than satisfied. Amazingly, almost all of them have been multi-site/single-host GoDaddy shared hosting accounts, so I'm really glad I made all of the file and directory aspects of the client easily-modifiable with variables.