I had the same car with the same size wheels not too long ago. Everyone will tell you different things about "correct" tire pressure. The truth is that even manufacturer's recommendations are only an average, because pressures change radically with temperature. You can be riding nicely in the morning, then be bouncing around like a rock by midday. But for what it's worth, here are my rules:
1. Don't exceed the max pressure written on the sidewalls, or the minimum pressure stated on the door jamb. Lower profile tires don't always need higher pressures- it's not an absolute; it depends on the tire composition.
2. Start with the pressures recommended on the door jamb, then adjust up by 1psi increments to get the best possible ride quality under the most common conditions. If it gets worse, back it down a little. You'll know it's right when the ride feels comfortable and the suspension feels like it's in tune.
As far as tramlining, it depends on the tire. Assuming of course, your suspension is good to go. Some will tramline worse than others. Some will resolve themselves after some wear has occured. And with many tires, an adjustment in pressure can also resolve it, so factor that in when you dial in the optimum pressure.