I use valvoline synthetic dot 3/4 fluid and have no problems, although I haven't tracked the Z yet, just my old 350 and current C6. If you don't have a lot of experience, even the stock fluid will be fine, as you won't be pushing the car to its full limitations, but for peace of mind, you could change over to any synthetic.
I flush my fluid a couple times a year, but thats because I swap pads out and if I'm rebleeding, its no more trouble to flush than to just rebleed.
I use a motive bleeder, it works really nicely.
Pads are fairly easy to swap on our car, but once again, for a novice, you are probably fine with the stock pads, or maybe try hawk hps, as they are a dual purpose pad. Myself, I run hawk hp+, which aren't the choice of hard core racers, but they work better than stock pads and don't eat rotors up, so I will give up a little performance for economy.
As for tire pressure, run whatever is placarded in the door (35, I think?) I'm at the track right now in my corvette, so I can't say for sure. We had a Yokohama rep just today doing a tech talk and he said definitely go with placarded pressures with street tires. 4-5 lbs less with R compounds.