Is there an ARM (or RISC-V) SBC under 200 euros where Guix system either works out of the box or costs little effort to set up?

Guix also works fine on Pine64 boards. The Pinebook works (at least somewhat), but the RockPro RK3399 do well. These are all relatively cheap but you might have to figure out some of the quirks as you go (: I guess similar to @theesm 's reply most RISC-V boards ought to work (though I have not tested any of that in a while)

I guess the best board for you primarily depends on how you intend to use it!