You may be interested in this post. Which is indeed about the requirements of the computer in order to be able to play high definition video without a hassle. Several answers for this question may give you a clue on where to start.
Smooth fullscreen 1080p playback
Additionally, transcoding seems to be the choice for playing/editing these high definition videos. Check the information on the next link, which may help you to see how you can have your beloved memories into good quality videos (even for the net).
How can I maximum compress video files?
There are several questions and answers in this site which may help you to find the best and easiest way to transcode your videos.
Some friends and I are trying to find a way to have the best tools for video playback/edition, which is fully documented in this forum: Israel Remix Team May be you wish to take a look on it.