With the small caveat that I only use Word, it runs perfectly in WINE and has done for over a decade. I use it on 64-bit Ubuntu, and it runs very well: it's also possible to install the 3 service releases that MS put out, and the app runs very quickly even on hardware that is 15+ years old.
The service packs are a good idea. They improve stability, and make export to legacy formats work.
WINE works better than a VM: it takes less memory, there's no VM startup/shutdown time, and host integration is better: e.g. host filesystem access and bidirectional cut and paste.
Step by step:
1. Install WINE, all defaults from OS package manager.
2. Open terminal. Change to directory with Office 97 install files.
3. Run `wine setup`
4. For me: turn off everything except the essential bits of Word. Do not install OS extensions, as they won't work. No bits that plug into other apps. No WordMail, no FastFind, no Quicklaunch toolbar, no Office Assistant.
5. Enter product key: 11111-1111111
6. Allow to complete.
7. Install SRs.
8. Run and use app.