Where can I find example MS, IR, NMR spectra for teaching molecular spectroscopy?
An elder way would be the via book examples, like «Organic Structures from Spectra» by Field, Sternhell, Kalman, with dozens and dozens of combined exercises in a format like the following:



and currently available in the 5th edition by Wiley (e.g., here). There is a  related project of «Interactive Spectroscopy Problems» by the University of Calgary (here), too.

German VCH published years ago Peter Bigler's training course «NMR-Spectroscopy: Processing Strategies» (e.g., here) including a CD full of 1D and 2D NMR data, which comes close to your aim of interactive sessions to process fids till the plot.  Bruker's WIN-NMR included is old (think Windows 95 era, could be still 16bit), but the experiment-based NMR data should still be processed by current software.

Almost forgotton:  NIST webbook chemistry has for many compounds which may qualify as «easy» IR, UV (condensed phase) and mass spectra, too.  While not aiming to be a teaching set, there are options to download the spectra not only as picture, but equally in the JCAMP-DX format to process, e.g., benzaldehyde.