I recently came across the Acer 5, that runs AMD ryzen 3 with 4GB ram at 315$ on amazon. I did a bit of research (and that's my only experience with it) and if budget is a factor, from what I saw you can't beat this one. If you can buy more RAM do it. Make sure to use both slots to activate the dual channel, as it will perfor better.

I managed to find a post from someone that has installed Linux on it, with no issues. And another that did have issues, but that's probably someone who was quite noobish to Linux.

https://www.amazon.com/Acer-Display-Graphics-Keyboard-A515-4...