You will probably won't notice any difference, at least on smaller screens, because VGA allows to transfer HD videos as well. Unlike digital HDMI and DVI, VGA is analog, so the higher the resolution, the worse the quality of the video.

DVI and HDMI can do 780p and 1080p videos. The only difference is that HDMI can transfer audio as well as video.

The cheapest way is probably to get a video card with DVI and connect it to PC.

But I would buy a network media player that allows to play almost any video from your local network. It will probably cost the same as a video card with HDMI (or an adapter card with HDMI), but a network media player can be placed in another room, has a remote control and many other useful features. Besides it wouldn't matter whether your computer is powerful enough to show 1080p videos, because the player will do the decoding.