As you've been told, MP4 is by far the most obvious choice.
AVI is ancient, with massive file sizes.
ASF and WMV are both, like AVI, Windows-based file types, which some video players on non-Windows devices, such as Android phones, might not play well.
QTMOV files are designed to be played with QuickTime and might not play with some other video players.
MPEG is, like the equivalent JPEG for image files, the accepted standard, with MPEG-4 (= MP4) being the 'final release'.
When uploading files you need to remember that:
(a) ADSL technology means that the upload speed available on a phone line is only around one tenth of download speed which can be achieved ; and
(b) you're often limited by the capacity of the receiving server. (So if Facebook, Youtube or whatever is struggling to cope with the number of uploads it's receiving, it won't matter if you've got the fastest upload speed in the world. Your phone or computer can't send the data any faster than the server at the other end can accept it).