A cheap 4k TV will probably look worse than an older 1080p TV since the price precludes good video processing, OLED consistently has the best overall picture quality but is costs more.
A 1080p plasma TV still looks excellent and doesn't require all the processing it takes to make an LCD panel look good. Great black levels without tricks. No issues with speed and refresh rate at all.
The only display that you still have a choice is in projection. You can still get a very good 1080p projector.
HDR is the only new TV tech that makes a real difference in picture quality and that is even more limited in content. It's also changing with different standards many of which no TV can yet fulfill. To get the added lumens needed they push the panels as much as they can screwing up the color.
4k isn't really visible at the normal distances that most people sit from their TV.