1) pointless to speculate on new GPU's until we have more details.
2) something better? RX-580 is pretty good, not the best but it will get you most of the visual fidelity of even really demanding games like Far Cry 5 (the difference between "HIGH" and "ULTRA" is often quite small.
3) Monitor?
Monitors are expensive so what budget?
*My advice is put the money into a good Freesync monitor then just stick with the RX-580 for a couple more years.
https://pcpartpicker.com/product/sqp323/acer-monitor-xf270hu
or
https://pcpartpicker.com/product/c298TW/asus-monitor-mg279q
Key specs:
2560x1440
144Hz
IPS
Freesync
Then simply tweak the game settings towards the FPS goal. Since it's asynchronous the monitor refresh matches the FPS (or is a multiple if FPS is low such as 28FPS becomes "56Hz" or two refreshes per frame.)
EXAMPLES:
a) run Tomb Raider at either 1920x1080 or 2560x1440 plus the optimal visual settings to make it look best at 50FPS average, or
b) run OVERWATCH at closer to 100FPS (to be more responsive) and tweak settings accordingly.