Linux

I'd recommend against any of those choices.

• Puppy Linux: It's a solid live boot environment but it's not really ideal in comparison to the major distros on a permanent install.
• Alpine Linux: Since it uses musl instead of glibc, you're likely to run into problems
• Linux from scratch: Going through LFS is a great way to get a solid understanding of Linux, but unless you want to spend more time maintaining your system than using it, it's going to be a frustrating experience.

Try one of the distros others have suggested.

Edit: I checked the specs on that hardware and yeah that's going to struggle. Maybe Alpine would be ok. It's fairly easy to spin up and might be fun to play with on that hardware. You'll probably want a fairly large swap if you're planning on using a desktop environment.

For starters, consider another distro if you want to make things easy on yourself. Alpine is probably a poor choice unless you have a reason to use it. I guess you could use it as a desktop if you really want to, but it’s more geared for containers and embedded devices. It uses musl instead of glibc so you will have problems running software that isn’t packaged for Alpine. The issue with Puppy is you will have a hard time getting help when you need it because it’s kind of a niche distro.

For your first time, you’re better off using something more mainstream. You are going to run into some issues and it’s a lot easier finding solutions for popular distros. Debian would be a fine choice because it’s widely used and runs great on older hardware. Beyond that, you could look at Ubuntu, Fedora, PopOS and Mint.

May I ask why you, as a beginner, specifically chose one of those distros instead of more "mainstream" ones?

Puppy Linux's main use-case is to be a live ISO, that doesn't need to be installed to run. It doesn't mean it's not a good idea to install it, but I think if you want to use an Ubuntu derivative, there are better options for a beginner like Pop or Mint that would let you install a lightweight desktop environment like XFCE, LXDE, LXQt and so on.

Alpine Linux is specifically designed to avoid all the core system tools that are pretty much universal on most other distros like glibc, systemd or GNU tools and libraries, which will make your life hell as a beginner if you need to troubleshoot anything as most "universal" documentation like the Arch wiki would be at best partially relevant, at worst useless.

use linux mint or pop os

You can install any general purpose distro (debian, opensuse or one of that others suggested) with a lighwwight DE (LXQT, Xfce, MATE) and it will work well. However when you run a browser and open several tabs with heavy websites it will become very slow. It does not matter what distro you use. You need 8G+ of RAM for comfortable web serfing nowadays.

If you go with Alpine, the general setup instructions should be OK and similar to other distros.

Get the image on a USB, boot from USB, run setup-alpine and choose system-disk mode. Possibly encrypted if you think you need that.

After install you'll be dropped to the terminal again.

There are some post install notes here https://wiki.alpinelinux.org/wiki/Installation#Post-Installation but you can run setup-desktop and get it to install a usable Xfce desktop, for example.

The LXQt DE is a good choice for older devices. The wiki has a guide for it but needs a slight update. It should still work but may require switching to edge.

Puppy Linux is a fine choice too if your computer is a little on the old side. Lite, Peppermint, Trisquel, antiX, and a slew of others are worth looking at.

Try Zorin OS, it has cool design, and is pretty stable because it has an outdated kernel and stuff.