Of the games you are playing now, find out which cards plays it best. Then you narrow down that list to cards in your budget.
The problem with a question like yours is this, you're asking for 'good' and 'low budget'. Those are two opposing things. "Relatively"? Relative to what?
Focus on the games. A 1060 runs the racing games that are out now and runs them well. A 1060 6gb should be good for 1080p gaming for quite a while, but you never know for sure until those future games come out.