as a project I want to turn a last-gen console into a retro gaming pc and a spare linux box. I'm curious which is the easiest to install linux on.

It doesn't have to run it's original software. if it's easy to make modifications to, that would be a plus (maybe a bigger hard drive)

what setup can run the largest range of emulators.

If you were doing everything from scratch what would you do?

Get online and start reading. I'll bet there's guides up there. Read a number, and follow the best.When you ask about issues, add a link to the guide and how you became unstuck.

Success with online consoles varies widely as some of them go out of their way to make things messy

What do you mean by 'last-gen console'? I understand that (technically) the Xbox One and PlayStation 4 are 'last-gen' (but good luck finding anything newer at non-scalped prices), but they aren't all that distinctive from the 'next-gen' Xbox One Series or PlayStation 5 - I also understand all of these machines to have locked boot ROMs which will make this task kind of a pain. End of the day it also won't be very exciting - the CPUs in these things are not very exceptional, and will be pretty awful for 'PC gaming' - you can get an Athlon 5350 for AM1-based boards if you want to re-create the experience with 1% of the hassle. Or go get something with better single-core performance/higher core clocks and have a better overall experience. If you're meaning 'last-gen' as Xbox 360/Playstation 3, that's going to be substantially more awful to deal with, because those are non-x86 systems with very little RAM (I believe only around 256MB total). Again, for 'retro gaming PC' you are better off buying some PC hardware. If you want to emulate really ancient stuff, get a Raspberry Pi.

The latest Raspberry Pi (4B or 400) with 8G ram is not that terrible at anything. It runs both Ubuntu 20.10 and Fedora 33 (full installs) with a quad-core processor at ~1.5 GHz so works well for a lot of things.

At less than $150 for a full kit with case and power supply it is also not unreasonably priced.

No I didn't mean to imply the RPI4 (or any RPI) is terrible; a lot of very old 8/16-bit platforms and old consoles (think old Nintendos or Segas) have full emulators available for RasPi (usually running on an RPI2 or RPI3) and its a *much* cheaper (and better documented) way to get into that than many other options.

As we're talking about the Pi 4B, it has surprising strengths and weaknesses.

• It sucks at CPU-intensive loads: 2 hours for an (admittedly huge) distro kernel.
• The 1.5Ghz can be overclocked. 2.0Ghz seems safe, I've heard that after 2.2Ghz, voltages need to be fiddled with, but it has been got up to 2.8Ghz. Extreme speed like that usually lead to disaster, but YMMV.
• Apparently the Mesa vulkan driver compiles for Arm and provides unexpectedly respectable 3-d graphics.