Hardware support for GPUs in based on compositor. X11 supports them better but Wayland is faster, both are available on most popular distros and swappable via a logout login.
Modern looks can be done with desktop environments like KDE and Gnome. Both are good, but KDE is more customisable.
If you don’t want to compile stuff yourself every now and then then choose Ubuntu or Fedora based distro.
Having the freedom to install anything you want is a fun requirement. If you mean literally anything then Vanilla OS might suit you since you can use all package managers but you get less modern features with it. This gives you 20 year old apps stuff that only works on some fringe dead on. If not that extreme then Ubuntu based is a bit better than Fedora based in those situations.
Ubuntu is nice and all but you’ll have to follow a guide to add flatpak support otherwise a very good distro.
So here’s a suggestion list from me:
KDE Neon (Ubuntu based on LTS versions)
Fedora (Gnome or KDE variants)
VanillaOS (if edge cases)
PopOS (New kid on the block. It’s just nice)
I recommend downloading whatever interests you and start them up in a VM.