Access 2003 or 2007 would be just fine for the scenario as long as you had an Access developer who was up to speed on how to develop for client/server with large user populations.
Access 97 is still an awfully nice version of Access. I think it's the best version ever produced.
But it is out of support and predates the alteration of default permissions in Windows implemented with the release of Windows 2000. This means that it has some problems in installing with its default permissions (it expects write access to its application folders and registry keys). An installation script can easily alter these appropriately, but you're still left with problems in certain contexts, like trying to run it in Windows Terminal Server/Citrix, where it very often just completely breaks.
I would like to hear an explanation of exactly why someone would choose A97 for new development. Of course, I may be misinterpreting. You may be asking about an existing app, in which case I'd go with "if it ain't broke, don't fix it," and then ask exactly what it is that is perceived as "broken." Those things can be fixed, though it's unlikely that simply upgrading from A97 to something more recent is going to do the job.