So i stand corrected, these display adapters have been improved with time (shocking, right?! :))
This one displays up to 1440p - it's USB 3.0 Type A to HDMI. I don't have a clue what refresh rate the adapter supports but if you do a little bit of digging you should be able to find out with relative ease: https://www.amazon.com/CableCreation-SuperSpeed-2560x1440-Compatible-Resolution/dp/B013G4CHD4/ref=sr_1_1?s=electronics&ie=UTF8&qid=1501860336&sr=1-1-spons&keywords=usb+to+HDMI&psc=1
There is a couple HDMI ones like this one but the reviews don't seem as great. Otherwise yeah you would need a vga to hdmi.