A quality 1400p monitor is $700. There is no 4k monitor worth buying for $350 .... With your budget, I'd recommend the 1080P VG248QE.
Until DP 1.4 compliant monitors arrive with fast enough screens, 4k just isn't ready for prime time.
AMDs Freesync and nVidia's G-Sync are not comparable technologies.
Freesync is a frame synchronization technology useful for AMD cards.
G-sync is a frame synchronization technology useful for nVidia cards but also includes a hardware module that does ULMB.
What GPU do you have ? ... unless it's a 1080, you don't have the Horsepower for the latest and upcoming PC Games.... RotTR only get 40 fps at 4k. This is what we generally recommend for GPU + Monitor Combos
1080p - AIB GTX 1060 + Acer XB241H ($700 for combo) or AIB GTX 1060 + Asus VG248QE ($530)
http://pcpartpicker.com/product/HPX2FT/acer-monitor-xb241hbmipr
1440p - AIB GTX 1070 + Acer XB271HU IPS ($1,190 for combo) or AIB GTX 1070 + Asus S2716DG TN ($970)
2160p - Until we see DP1.4 and 120 Hz, I think we have to give up too much to get to 4k. If ya want 4k, I think we need to wait till January 2017.