Graham (Apex) said something when I first started that stuck with me and I even do now days. Do the first several laps at no more than 80% .. then look to have a a couple of screaming laps then warm down. This way you can build up to it in both your car and your mind. About the others, most of the regular track dayers will spot people and not try and late brake or set up if someone looks like theyre new at it. All that will happen is both will end up in a big mess. So Im yet to see anyone whos been bad. When you first start the scarier moments are look out for are race cars (or people running slicks / big brakes etc) They can outbrake, take proper lines, power past and out corner any car. The best thing you can do is on the straights take quick glances every few seconds in the rear vision mirror and hold your line. Its their problem to get around your car. Even in a corner if theyre sitting up your a*s just hold your line and they will go around. Takes a bit to get use to it if your new to it.
Like wise if you are the fast car, at public days always leave a gap for errors of you and the person your over taking. When your learning, leave DSC on. While it cuts in on the track a little too much it keeps you safe while you learn your chassis and its limits. Seen quite a few people who turn it off after one outting and end up in the wall powering out of turn 1 or turn 4 of hamptons.
Car wise, make sure your brake fluid is in top condition. Use a great dot4 or 5.1 fluid. For this I use motul as its rated for race temps .. even your road car will get up there in temp. The last thing you want is screaming along down the straigt and you boiled your fluid and created air bubbles in the lines .. hit the pedal and nothing. It _really_ knocks your confidence when it happens .. Pads, just make sure theyre in good condition. OEM pads are great around the track, cheaper aftermarket pads and discs will warp after time.
Road tires will start to over heat pretty quick and loose grip at higher temps. Cheaper tires will start to have side wall issues. Tire pressures should be around 34-36psi or 38-40+ on low profile tires.
Engine oil and filter should be new or near new.
Cooling system should be checked and in top condition
Other things like trans or gear box fluid should be looked at.
For the next track day, I always change my brake fluids and engine oil gets a really good look. If it smells burnt .. it gets binned.
typing all of this stuff mainly as a FYI for others