Dropping a GPU into a refurb is the best way to get maximum gaming performance for cheap, right this minute. But you'll need to be prepared to toss the entire thing in the trash when you decide to build your "good" rig, later.
I'd not be as fast to dismiss the RX550, if it's in a box like this one:
http://www.microcenter.com/product/503298/Pavilion_580-137c_Desktop_Computer_Refurbished
That's a hell of a system otherwise - depending on what you're doing
besides playing games, a fast CPU can be....
nice. You can always upgrade the GPU later, finances permitting.
As an alternative, I'd be checking out local mom'n'pop independents that do custom builds. You can probably get an "intro" level ATX tower for ~$500 that might not run GTA V at max-everything-settings, but which will be a good foundation for upgrades once you decide to BYO. (Replace the low-end CPU with something faster, like Pentium->i5, drop in a better GPU, etc.)