when you say 4k, do you mean 4k @ max resolutions no compromise everything on or do you mean you can compromise.
Because right now, nothing out there can do 4k with all the eye candy and expect 120fps. In that situation 1080ti or Titanxp.
1080 will do 4k with compromise, ie lowering some settings to get higher fps, but it can do it quite well.
1070ti if you overclock the hell out of it can do 4k with compromise on certain settings, ie turning some setting to minimum from high.
1070 and your are going into just barely be able to do 4k at acceptable frame rates. 1070 is mroe a 1140p card.
maybe wait a few months if you can for the 1170 or 1180 and give you a chance to save more, those cards should theoretically be better able to deal with 4k. If you are serious about your 4k gaming i would say wait and save up more, 4k on "budget is not huge" just not possible unless you somehow manage to get a great deal from somewhere.