Are you an experience Linux user? Alpine is a bit of a curve for installation and setup. As with what everyone's saying, any distro that's easy to install that has LXQT, LXDE or XFCE is worth trying out. Personally I still think XFCE is decently light weight and would recommend trying it.
One you get comfortable with Linux, distros like Alpine, Void or even Gentoo are good for advanced mode. But unless you're a coder or infrastructure programmer that likes tinkering, sticking to a major distro (Mint, Ubuntu, Debian, Manjaro, etc.) is probably the way to go. Try each one of them out on the laptop for a day and store anything you want to keep on a USB drive before deciding.