I'm glad you got that sorted.
HDMI has a some advantages over a standard VGA cable, for one thing it can carry both video and audio signals simultaneously, which is handy if your displaying to a large-screen TV which has built-in quality speakers, so instead of having to hook up two cables to the monitor (audio & video) you only need to hook up one if it's HDMI.
Image quality is also better than VGA because the signal is digital (VGA is the inferior analog signal). However you'd be hard pressed to tell the difference for everyday Windows use. It's keen gamers who see the difference in image quality, for them HDMI or DVI is their first choice.
The other advantage is that an HDMI cable is much thinner than a VGA cable, but it does have one downside - - unlike VGA it doesn't have those retaining screws to stop it falling out or getting pulled out.
I tried the DVI connection (which is also digital like HDMI) from my graphics card when I got a new monitor, honestly couldn't discern any difference in image quality compared to VGA, but then I'm not a gamer and I don't spend big bucks on a high quality screen either, would be waste of money for my needs.
You don't need more RAM to use an HDMI-equipped graphics card.