Hey, welcome to the Crystal forum!
Crystal packages are available for most major operating systems/distributions/package managers (see https://crystal-lang.org/reference/installation/). SQLite should be even wider available, as well as most common IDE software. You just need to pick what works for you. Crystal plugins exists for example for VS Code, Atom, Sublime Text, JetBrains. (I guess it might be good to have a separate overview of IDE options).
So the only real restriction from your requirement list are rolling releases. Popular choices for this are Arch Linux and derivates (such as Manjaro), and Gentoo. Arch & Co are used by many in the Crystal community (see also What's your favourite/recommended Linux Distro?).
But in the end, it depends on what system you want to use, ant not as much what works with Crystal…