For a branded system I’d recommend a Dell XPS desktop, but that’ll be pushing the budget for latest models. Might find a deal in the Outlet store though.
I’m no expert on other brands these days, but basically look for an i7, 8GB+ memory, decent independent graphics card, numerous expansion slots and a few hard disc bays so you can slap in more or change the default to an SSD but keep the existing hard drive for data (SSD for OS, hard disc for data). Unless you can find one that ships with an SSD built in, but wouldn’t be too fussed about that.
Don’t worry if it comes with Win 8.1, you get a free upgrade to 10. Just check the manufacturer has all the drivers for 10 or certifies it for 10.
Barebones then obviously up to you. Been a long time now since I’ve done one. I used to do them all the time, case, motherboard and build it all up, but it just got a faff and then I started getting out of date with latest tech. Used to have a lot of stability problems too and often juggling different components to find something that works together without crashing.
Linux adds complexity as you’ll need to check all the hardware has a suitable Linux driver.