Start with this free download from Aircraft Spruce (scroll down to the PDF):
https://www.aircraftspruce.com/catalog/bvpages/soundproofmanual.php?clickkey=7775
Then....
Step 1 - what is the condition of the interior (sidewalls, headliner, carpet, etc) and what's the condition of the material behind the interior?
I had original 1968 vinyl over cardboard interior panels and what looked like fiberglass batten behind it. Very obvious, looking at the cardboard, that at some point, the interior got wet. Soaked. Fortunately, only the interior and there wasn't any corrosion to the aluminum.
Step 2 - is there anything you can remove to reduce weight, such as unused equipment, wiring, etc.
There are any number of sound deadening materials that are FAA approved (fire, combustion, smoke particles and toxic fumes) that you can install yourself behind the wall panels and above the headliner.
DO NOT USE ADHESIVE-BACKED FOAM ON SIDEWALLS!
Don't ask.
It's ok above the headliner but there's too much structural, wiring, cables and hoses on the sidewalls. Once you place the foam with the adhisive, it's not coming off with out destroying the foam. It fits in nicely without adhesive and the sidewalls will hold it in place. But if you insist, get a small can of FAA approved adhesive and use just tiny bit in corners to hold in place. Doesn't hurt to put the material on the back side of the baggage area, either.
I used this - 1/2 in thick. The mistake I made was getting the adhesive version. Dumb.
https://www.aircraftspruce.com/catalog/appages/soundproofinstall.php?clickkey=7775
Total for the cherokee - everything except the headliner - was about 10 pounds. Worked out to be a wash because I had over 10 pounds of ancient wiring and crap removed. Only did the front half above the headliner because I didn't want to take the whole thing down. Easier to peel back the front couple feet.
Another advantage - temp control. It's a bit warmer in winter and cooler in the summer. But...engine noise comes thru the windshield and firewall. There's not much you can do other than thicker windows. A thicker barrier against the firewall will help some.