Simplest way to Properly Transfer Domains?

Hi I know absolutely nothing about domains, hosting, or anything of the sort. All I've dabbled in is some front-end (?) html for website design.

My uncle has been wanting to update his website for the past ten years and recently he reached out to me to help him, and he's using network solutions (which I've read is really bad?). First I read some really good things about the Cloud Flare free plan, but i read that domains can get stolen easily there and that pork bun is better?

I also cant seem to find the monthly fees for network solutions that he's paying either. He just wants a really, really basic static site for uploading his journals. He also wants a couple of domains for them to be hosted under.

I was thinking of just transferring the domains to cloud flare and making a simple static page for them to go under but I don't want to risk him losing his domains.

How can I best go about this? Please help this amateur!