There’s a method using systemd-sysext that would work well for this on any distro without dealing with poking holes in containers. One of the gnome folks blogged about it recently here: https://blogs.gnome.org/alatiera/2023/08/04/developing-gnome-os-systemd-sysext/
It might be more web design leading but my company’s designers have switched to Figma, which is web based and has allowed me to work with their files for dev on Linux.
Another alternative I like is zim. I feel it’s snappier and less fiddly than oh-my-zsh.
If you really don’t want to even be encouraged to touch the command line but do everything through a graphical software store (that’ll be gnome software) while still having access to everything you need, one of these two is currently the way to go. I just came across this older article comparing them, and it seems for the new user openSUSE Aeon (micro os, formerly) wins out in minimal fiddling.
What software are you using to plan it out?
Linux can definitely make that thing fly, although the biggest limitation will be RAM - not from the desktop environment you choose, but from the web, depending on how many and what kinds of websites you rely on (for example I regularly use 20-30GB of my 64 through figma, pitch, Google docs, notion, ClickUp, and sites I develop that tend to be video and image heavy). Were I you, I would prioritize the 8Gb ram upgrade.
Aside from that, which distro you choose won’t make a huge difference. Some claim desktop environments like gnome and kde plasma are too heavy (I assume they mean in graphics processing and ram usage) and will insist on something like xfce or sway. Those are invariably very fiddly to set up, so if you’re a beginner, I would recommend sticking with gnome or kde despite. These will be the default on the distros you mentioned. Mint MATE edition would be your best bet for a classic desktop environment that might tick the “lighter” check mark if you really must.
There’s not much below $500. Here’s what I could find:
Another option is to buy a Chromebook, or look for a second hand several generation old Lenovo Thinkpad Carbon X or Dell XPS Developer Edition. The latter is your best bet for not getting something underpowered, but also carries more risk of it breaking down sooner with no support possible. You might be able to find a first gen framework 13 second hand which can be fixed if something goes wrong, but it hasn’t been around so long that they are that cheap. Still someone might want to get rid of it and low ball it.