I'd suggest looking at a single-use distro, like GParted.
It's a rather minimal distro, but comes with the standard set of utilities, that you mentioned (and a couple more). Fits nicely on a small USB drive, too.
Another such tiny distro is TinyCore. At just 16MB in size, it's a minimal, but complete distro, with everything you might need, when you know what you're doing. Even at that small size it comes with a graphical interface. There's an even smaller release simply called "Core". At just 11MB, it comes with just command line interface, but it otherwise a small but decent OS.
TinyCore and its variant TinyCore Plus (106MB) are my go-to distros for very old computers. Like mid-90's laptops, or early 90's desktop computers (think 486'es).
All TinyCore variants boot from USB sticks or optical media.
Fli4l is another niche distro, geared to work as a small server for home use. It's supposed to support telephony, etc. Similar to OpenWRT, so not sure if you'd be happy with it.