Usually I start with changing the toe and sway bars after I've purchased suspension upgrades. I find the default spring setups to be ok.
Steps.
Purchase track suspension or motorsport suspension, and then buy a tune slot for 100c. This will then automatically install the upgraded suspension and you get a decent default setup. You'll see the default setup will have lowered the car and stiffened the springs and added camber for you. This is a good baseline.
If you don't buy a tune slot I'm not sure if the suspension upgrade will get applied so I think it is important to buy the tune slot. From here I touch up on the toe and the sway bar to suit your driving style.
For example: Sway bar settings
1. Stiffen the front for understeer.
2. Stiffen the rear for oversteer.
Adjust the toe for how sensitive you like the steering wheel to be. Toe in for calmer setup, toe out for aggressive and more sensitive steering.
Project Cars 3 tuning is really impressive. The more I play with tunes, the more I am appreciating this game.
Try to upgrade a NSX, RX7, GTR, Supra into a Road C class car and use it for Road C cali counter event at Willow Springs. You'll find that by fine tuning the suspension you can really lower your laptimes from a good suspension tune.