CommonMark, Kramdown and GHFM are 3 kinds of markdown.
Jekyll config uses markdown: kramdown as the default. I leave it out my config.
I’ve been using Jekyll for years and never needed to switch to another format.
I don’t know if you can set the in your IDE and how much benefit you’ll get.
I use VS Code with a Liquid extension installed. And I set up per project for .md and .html files to use liquid highlighting. Haven’t bothered to check if it handles flavors.
Regarding the target stuff, that is very specific to Kramdown. I would not count on your IDE to render it in preview pane but as long as you can see the source code in your IDE you’ll be fine. Also looking on GitHub itself won’t help but viewing a Jekyll site will be fine.
Some flavors of markdown will require white space around say bullets or headings and others won’t care. In particular I had issues using either Sublime or maybe PyCharm, where my markdown preview looked good in the sidebar but rendered funny in GitHub. I adjusted my markdown code habits to accommodate for this by writing the most compatible code and checking results on GitHub and IDE.