My preference is ASP since it has been around longer but PHP seems to becoming very popular.
What platform are you on, NT or other?
ASP is native (and free) to NT, available on Linux and UNIX but it is not free.
PHP is free but not on very many ISP hosts. From what I remember about PHP is that it was initially created for non-Windows servers and then ported to NT.

ASP does offer the benefit of creating COM objects which is essentially your own VB or C++ applications for the web (largely used for database work). PHP does not have this.

Your application sounds interesting and will require some interesting coding and will have some hairy processor issues, if there are many people accessing this app. at once.

Good Luck!

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Cheers,
L. Drolet