The current codec of choice is certainly H264 (or H.264):
http://www.doom9.org/index.html?/codecs-final-105-1.htm

Just search for it and watch some examples. However, everybody uses MPEG-4 nowadays and all those codecs are just variants. So any of them is virtually as good as the others. As a rule of thumb expect at least 250 MB for 30 min. of video at good quality.

The resolutions depend on the source material of course. TV recordings (this means digital and usually HDTV nowadays) have a typical resolution of 640x480. If the source was a DVD it's 720x480. Random "clips" often still have only 320x240, the same applies to very old files (usually MPEG-1). The latter cannot really be "enjoyed". I'd only use it when picture quality does not really matter. One problem with older encodings is that they tend to show "blocks" which is really ugly. Modern MPEG-4 codecs don't have this problem, you can hardly tell it's digital if properly encoded.

Unfortunately, the filename itself seldomly tells anything about the quality. Sometimes the codec name is added to filename - of course this could be a lie/mistake. AVI can really be anything from custom codecs over outdated MPEG-1 to modern MPEG-4. If you're lucky, there's a Bitzi entry for it, otherwise look at the size, download a few megabytes and check its quality with your video player.
The same applies to MPG resp. MPEG. It's really just a container. It often is crappy MPEG-1 but recently I've noticed it's also used for MPEG-4 encoded files again. It can help to look at the alternate filenames. MP4 is the "official" filename extension for a MPEG-4 container and also
used.

MKV (Matroska Video) and OGM (Ogg Motion video) are also newer and popular container formats. They usually carry high quality video.

The largest resolution I've seen was some 1400x1024 file. The resolution may be misleading though. Depending on the encoding (especially the bitrate), the effective resolution might not be higher than 640x480. So it may look good but not as crisp as the real HDTV source - which may give you a false impression of HDTV. It requires a larger computer screen or HDTV monitor (a usual TV screen won't do) anyway, to see the difference between HDTV and a DVD.