Is it fine just to get 19" or 20" for this VGA?
Or should I at least get 21-22" in order to get 1920 x 1080 resolution?
Don't get a monitor which only has VGA. Get the one which has DVI or HDMI output. Since you have a good gpu I suggest you to get above 21" you will have a great performance, if its HDMI output it will be very good. You will see the difference when you are playing games or streaming videos at full HD resolution