You can use any format you want. Servers don't care
I'm not sure that I would particularly recommend either of these formats right now, though - but without further details, it's hard to say what format would be best for your users.
RealMedia has rapidly lost popularity. AVI limits you to Windows users. FLV seems the hot web video format right now, driven initially by YouTube, but subsequently by it's rapid ascent to ubiquity.
You wouldn't shoot in either of these. Most common and practical these days would be DV, which is available in a wide range of cameras from inexpensive consumer models to semi-professional cameras used in low-end news gathering. DV is transferred to your computer over FireWire, and then you can convert to a target format.
The Wikipedia article provides a good introduction to DV:
I certainly wouldn't recommend today shooting in analog and then transferring to your computer through a capture card. That's old-hat, poor quality, and painful.
There are a large number of tools for converting between video formats. A popular free, open-source one is ffmpeg.
You will probably have to do some video editing along the way. For best quality, it would be good to edit in DV or in some format that is able to preserve the quality of the original. As a rule, formats that do inter-frame compression (DV does not) are not a great choice for editing. Although widely-used, MPEG (2 and 4) is really a poor choice for editing, though it can be a decent format for delivery.
There are quite a number of consumer cameras today that shoot in MPEG4, but I would avoid them for the reasons stated above. If quality matters, shoot in DV.
The advantage of MPEG4 cameras is that they compress sufficiently that most/all use solid-state storage, resulting in a more compact camera. Most/all DV cameras use a tape (which records in a digital format). As far as I know, all DV cameras include a firewire interface that you can use to transfer to your computer.
Bring plenty of disk space.