Does DVI to VGA monitor connection have the better display quality

Theoretically, DVI-DVI would be your best bet, using a DVI-VGA adapter is a step down but both are still better than just using VGA-VGA. Having said that, the money you would spend (if it's an issue) may not be worth the increase in quality, since the difference is noticeable but isn't that significant for most applications. If you're going to spend money on a new monitor, I'd go all out and get a video card and monitor that can handle HDMI. =)