Going with something stable is good. That's why I'm using SDL 1.2 rather than 2, although that's also because I created my latest engine five years ago,
when SDL2 was much less stable than it is now. It's been in development for years and is a fine place to start these days. (By comparison SDL 1.2 is really showing its age, but it does still work well enough.)
SFML is a fine option, too; go for it.