To help improve the precision of my flying, I'd like to
overlay the GPS track of my flight on a chart so I can
compare.


Although I don't recall what the most 'usable' program is right now, my
guess would be the OziExplorer.

Yes, OziExplorer is perfect for this. The steps involved are acquisition of
a scanned approach plate via whatever means (if you have Adobe Photoshop you
can import the PDF files of the NOS charts on AOPA's website), import the
image into OziExplorer and calibrate using up to 9 points (fixes and VORs
work just fine, anything that you can get an accurate lat/long for), then
download the track from the GPS into Ozi.

Here's a sample: http://64.203.15.192:81/KSUS-ILS-RWY-8R.gif