Linux

To be honest, I wouldn't on a 2Gb laptop. It'll run Linux just fine but the minute you use a browser or office suite you'll have memory problems.

Last time i searched for "lightweight" linux distros (for an old Thnkpad) the ones i saw recommended the most were: TinyCore, Puppy, Porteus, Absolute, antiX, Q4OS, Slax,, Sparky, MX.
I saw Bohdi and other Ubuntu-based distros suggested quite a lot as well but my definition of lightweight means under 1GiB usage.
For a DE go with XFCE or some other lightweight DE.

Puppy would fly on there, or even DSL 2024. Heck, both those distros would fly even on a Pentium 4 of all things.

for linux and the most basic of basic tasks, i'd look at peppermint. it's what i put on all the old crap here with 'marginal' specs that choke on windows. debian stable xfce based. base install is pretty sparse, not even a browser is included initially. a utility pops up after first boot to facilitate installing a browser, media player, and a few other things if you want them, or the entire debian stable repository is also available. one thing of note. with only 2gb ram, it's gonna be tight, whatever he runs on it.

his use case is screaming for a cheap chromebook, though. so at least consider that instead. an old laptop like that might make someone a nice little pihole or something, if it's not ready to be put down for good.

Debian, lxqt and x11.

If you can get an ssd in there then there’s some zram or something or other that can make it even better.

Your biggest problem is the amount of RAM, not the cpu. Some Linux distros would fit nicely on 2gb with a few native apps open, but the moment you'd want to browse the web, all hell will break loose, as each tab will take hundreds of megs each (youtube takes between 600 and 1200 mb of ram). FYI, even if chrome/ium is hated in these parts, it uses less ram than firefox (there's also a setting to use even less ram).

I'd suggest you use either Alpine Linux with xfce (240 MB of RAM on a cold boot), or even better, Q4OS with the Trinity Desktop (fork of KDE), 350 MB of RAM. The advantage of Q4OS is that it's a debian, so it can run lots of .deb files made for debian. Alpine is cool and all, but it has bugs on the desktop (some of its package management has dependency problems).

A tip: to save ram, don't use background images, only a single color. You can save up to 50 MB of RAM that way, depending on the image you'd be using.

ZorinOS

Windows 10 has a bug with 100% disk utilization that goes away if you have an ssd. You should look into upgrading the ram to 4 or 8 gb. ddr3 ram is dirt cheap on ebay. It would probably cost $10-$15 for 8gb and another $10 for a 120gb ssd.

Debian is on the right track. XFCE might work - I remember it running pretty well on a laptop with 4 gigs.

puppy linux. ironically its made to run completely in memory but only needs like 500meg

Puppy Linux is what I usually see recommended for such low specs. It's also available with a Debian base.

https://puppylinux-woof-ce.github.io/

Puppy or Debian with openbox or another light wm , is crunchbang still a thing ?.

Raspberry Pi OS or antiX.

Mint.

It's extremely stable Linux for your grandma, that comes with every tool that she will ever use and on the cinnamon interface all those tools are exactly where she will expect them to be if she is used to using Windows.

I've gotten three boomers to use it and they hardly ever ask for tech support because it's so stable.

I think antiX would be a nice option. I installed it on a 20 years old laptop and it runs quite fast.

Upgrade that box or repurpose it for something else. Web bloat has made 2gb machines useless for browsing and 4gb marginal, if the user needs Google docs, put in 8gb or more.

honestly the distro doesn't matter so much as long as the hardware i supported. run a minimal desktop, disable CPU hogs and file indexing etc.

I used fvwm on Debian for many years on old computers. worked great. now I have kde/plasma on arch. my 10 year old laptop handles it fine...

alpine

There are plenty of distros for very low end pcs, but they tend to require more tech skills to use. I have experience with a friend in a similar situation. I installed with mx linux for her and she is liking it. The performance is pretty reasonable and it comes with various tools that make it easier for people with less tech skills. The only extra thing I did was install the 32 bit version of firefox, because it makes a huge difference in low ram devices.

Debian can be pretty light/small on a clean install and xfce should run fine on 2gb. Although the biggest thing is gonna be if the laptop has fast storage or not. Since its a celeron it might not be upgradeable, and if it doesnt already have an SSD any desktop will feel slow

Personally if I really wanted to squeeze all the performance I could for web browsing I'd go with minimal Debian and RiverWM but thats a bit more involved

AntiX or Alpine

VoidLinux

If your friend is not tech savvy person, i would go with Mint XFCE (maybe Zorin OS Lite). Surely, it will be not as lightweight as Debian, but it will be much more user friendly for him

If he actually feel comfortable tinkering with OS - along side Debian maybe Bodhi Linux or antiX? I tried both of them on one of (in)famous Intel-based netbooks with 512mb RAM and they worked quite well.

minios https://minios.dev/

With low specs like that, the experience will never be great, but with a very light desktop you can make it work. Debian is fine, but with some set up, Alpine could be one option. It's a really light distro.

I think Slitaz is still around, I always liked that for older machines, I was going to try it on an AMD C-50 laptop I pulled out of storage recently, except I don’t have time for messing around.

AntiX buy sadly all it's desktops only support x11.

Fedora.

It seems to be easy to manage and fast to install.

SUSE is slow to run and self-update.

Debian is far behind and Ubuntu seems to always have an issue during or right after installation.

Lubuntu has always been solid for me for low spec machines.

With only 2 gb of RAM it will be slow, there is almost no avoiding that part.