(listed in my personal order of preference)
1. Fatdog64
Puppy linux inspired, but really it's own distro. Built from the ground up (LFS & BLFS), with careful attention applied to minimizing dependencies. Resulting in a very lean setup.
They use Slackware's basic pkging tools, but again - they build everything from scratch. So you can think of it as an "alternative minimalistic Slackware", done by someone other than Patrick V.
The layered filesystem is done a bit better than puppy linux (IMHO), and unlike puppy, it can be configured as a proper multiuser system.
The more you delve into Fatdog's innards, the thoughtfulness behind its basic design shows through. Included are a range of scripts to quickly run fatdog within fatdog (to compile and test new pkgs, or just to sandbox an app, or whatever).
Also, the entire set of build "recipes" used to create the set of slackware'd tarballs which make up Fatdog are themselves provided.
For what it's worth, I moved some of my boxes onto Fatdog many years ago, after 10+ years of being purely on gentoo.
2. puppy linux
VoidPup is my favorite here.
3. pure Slackware?
Porteus.
I used this quite heavily a decade ago. It has been refreshed to Slackware15. Portuex ( a derived fork, see it in the portues forum) tracks slackware current, so it should be very up-to-date.
4. Debian-based?
AntiX (very lean, with runit and nicely pre-configured window managers) or MX (more mainstream debian).
You can think of them as 2 flavors maintained by essentially the same group of developers.
Consider AntiX, with repo's switched to sid.
It may be worthwhile to look at the big distributions (Fedora, Debian, SUSE, Arch, etc) and see if you can find anything that fits your taste.
It can be as simple as 'inserting a coin and pulling the lever'; I recall listing some extra packages and running a command to download the assets/press the ISO.
Nix(OS?) tries to be something like this IIRC, but it's less "provide something extra" and more... start by defining the nucleus.
I also have a complete system installed on a 64gig or greater USB stick, as a portable backup system. But I have rarely used it. I say 'stick', but it's a tiny little flat tab thing about 2cm by 1cm by 1mm. (looks a bit like two micro-SD cards stuck end to end.) It lives on the key-ring holding my bank-fobs.
That's the bit that used to annoy me a lot. Invariably I wanted to add something to the LiveCD, or to transfer a largish amount of data. The read-only aspect of things got in the way.
With a complete 'system on a stick', you can install extra packages if you want, you can even do development at a pinch, mainly bash scripts.
I use this together with some iso suggestions of my article: https://pilabor.com/blog/2022/01/the-ultimate-boot-stick/
Puppy is great though.
No other distro has this issue on my laptop, but then again, they all use/support Wayland.
Is there a Puppy out there that uses Wayland?
Unofficial Puppy Linux derivatives are not very easy to discover. I found Vanilla Dpup by sheer luck on GitHub yesterday. (I had contributed to a previous distro by the same developer and was going through my PR and issue history.) After about an hour of testing, it seems to be the most practically usable current Puppy variant. (I am comparing it to https://debiandog.github.io/doglinux/ and the official FossaPup64. I haven't tried the official Slackware 15 version.) It's a shame I didn't know about it when I needed a live USB a month earlier.
I like how it has a 2000s-retro GUI theme that looks inspired by Puppy Linux 4, my favorite version in terms of visual design. Compare https://github.com/vanilla-dpup/vanilla-dpup.github.io/blob/... and https://upload.wikimedia.org/wikipedia/commons/4/40/Puppy_Li....
(Some other thanks also required i guess. Regen your machine-id. I use the auto-mounting partition types but if you don't (most people don't), update your fstab and kernel cmdline.)
I hope the GRML people are working on a new release, as it's been a year since the last one.