There are various ways to do it. By default github pages support jekyll so on new commits github automatically pushes those changes to your blog/website.
If you plan to go with something like Hugo you'll have to setup a github action which will do the processing for you. Example of such github action can be seen here(https://github.com/mzfr/mzfr.github.io/blob/hugo/.github/wor...)
In order to actually move, the best way is to convert your webpages to makrdown and then just put them in the github repository.
A quite well know blog post about moving from wordpress to static gh-pages is this(https://www.hywel.me/static/site/wordpress/2016/07/17/fast-f...). But I think this might be old so it may or may not work.
Below is the list of few more blogs about this process:
* https://www.logitblog.com/moved-away-from-wordpress-to-githu...
* https://blog.netnerds.net/2020/08/migrating-my-wordpress-sit...
* https://haralduebele.github.io/2021/02/10/Moving-my-Blog-fro...
All of these blogs did it the same way, setup gh-page on github and then from wordpress export your content to markdown.
My suggestion is if you don't have much experience with markdown & github pages then just go with having a simple jeykll blog. And you can choose themes from here(https://jekyllthemes.io/free)
