It’s doable but you should treat it more as a learning opportunity than a production system. Honestly, that’s old enough that a RPi might be able to run circle around it.

The Celeron 1011 is a 32bit processor, so Debian or Gentoo may be the only distributions that still support it and you will probably have to compile from source anything you want to run. A gig of ram was good for its time.

The Linux Unplugged crew from Jupiter Broadcasting are currently doing a 32bit challenge to see if such systems are still usable for day to day usage. It’s going to be interesting.

If you get tired of that, you can probably turn it into a virtual fish tank and Johnny Castaway machine. (1GHz atom, 1gb RAM, XP)

Worst case, give it a go, learn the process even if it can’t handle it, and you’ll be able to do it easier when you have a capable machine.

I wouldn’t dare to charge that old battery up. Some of them can start a fire.

Be aware that some old laptops had weird combined chipsets that Linux just can’t use… I tried putting Linux Mint on a friend’s laptop for their kids to use and the networking (wifi and cable) just wouldn’t work… it was something that only Win98 / WinXP could use (from memory).

So just try anything in case you just need to ditch it - as someone else mentioned, treat it as a learning exercise.

Go for a vintage correct OS for a challenge, try Haiku!

Alpine. But you are very low on the RAM. I will buy more RAM if I can (DDR2(?)).

No

DietPi (it runs on PCs)

Maybe. You limiting factor is going to be power and thermals. I started on a broken laptop and moved to a minipc when I first started.

Upgrade ram to the max and set zram and everything will be good to go

I don’t know about the whole 'arr suite but one BT client and PiHole should not be a problem. Provided you don’t seed hundreds of torrents, but even that may work out ok-ish depending on the BT client – some of them like Transmission or rTorrent are more efficient than qBitTorrent or Deluge.

Edit: oh and distro, any distro provided you disable unnecessary services. And I’m assuming you plan to use it in CLI mode only.

It sounds too slow. Save yourself time and sanity.

It depends on the size of your budget (if it exists at all). Your probably better off doing some e-waste dumpster diving. Shoot for something with a 3rd gen i3 / i5 or newer and at least 4gb of RAM.

That generation is when Intel added MPEG hardware encoder so it opens up a lot of options for self-hosting media servers.

Puppy Linux!

Xubuntu, Lubuntu, Gentoo, Peppermint…

Some others like damn small linux or nano Linux or Linux lite.