Install Mac OS X 10.3 on Intel Mac

No can do. Intel Macs can't operate using Panther; only Power PC Macs. Also, all Macs (Intel & PPC) can't operate on an OS lower than the OS that came on the Mac.

 Cheers, Tom 😉

You could consider getting a second, older Mac
and then have Panther 10.3.9 on it. Those may
be available at comparatively great discounts.

You can see in the free database from MacTracker
which models natively use earlier OS X versions
and then be on the lookout to rescue one of them.
See http://mactracker.ca to get this offline database.

{My preference is for Tiger 10.4.11; though a few
good ideas were dropped from Panther on the
way to Tiger. A few in the user interface and in
Preview (in 10.3.9) was better at image edits.
Simple rotations would 'stick' & work in email.}

Good luck & happy computing! 🙂