Don't go out of your way for freesync, Because price differences between non-freesync and freesync-capable monitors are not particularly deal-breaking, look instead for other specs of a monitor that would interest you, and consider freesync as a bonus if it is present.
Freesync monitors aren't very well regulated, with some monitors having outstanding freesync capabilities, while other freesync monitors have small ranges of FPS that are able to use freesync.
Instead, look for panel types (TN for cheaper, faster response; vs IPS for more viewing angles, colours, contrast), refresh rates (60hz is the standard, 120-144hz are more for FPS games), resolutions (720p for budget builds, but in this day and age, people may laugh, but let them; 1080p is the more common resolution; 1440p is a step up, but more expensive; 1600p as practically non-existent anymore, overtaken by 3840p (aka fake 4k, or UHD), or even gimmicks, which range from useful (VESA-capable) to less useful (3D-capable if that's your thing).