graphics card 4K for starcraft remastered?

I am due to build a new comp (dead radeon and dying 8800 GTX). have a 4K LG monitor with freesync. got this in advance to upgrade my sad 720 p tv.

now which graphics card can I run starcraft remastered on in 4K? minimum graphics card here. I am assuming this game will not be a normal 4K game which makes it kind of hard to gauge as to what the minimum would actually be. I am assuming I can easily get away with a cheap radeon card and with my freesync. I am leaning toward this option after having my sights dead set on a gtx 1070.

but the other question is: I am building this comp for the future as well. would it be a huge mistake to go with some cheap graphics card that will have trouble with newer games very soon when it comes to 4K.

I have a large backlog of old games and don't need to run all the new games at max settings. just want smooth 4K on old stuff for now. still trying to figure this out...