If you’re not looking to spend a lot of money. You could always just get a PS2toHDMI adapater.
http://www.amazon.com/gp/product/B00D875R5K?psc=1&redirect=true&ref_=oh_aui_detailpage_o00_s01
Just note that there is no upscaling going on here, it’s just taking the rgb signal and converting it to the hdmi standard, so if your monitor doesn’t read 240p signals, this converter won’t work miracles and bring it to 480p etc.
I have one myself, and it works pretty great on my ASUS V236H, there’s little to no lag on it either. I use it to play CVS2 on my PS2 and don’t seem to have much of a problem.