WOW...
To start off, what gears do you have? I didnt see a mention of anything other than stock, so I assume 2.73s or 3.08s. With street tires and stock gears launching off idle might not be the best bet. Bring the car up to 2500 RPM and slip the clutch. Coming out off idle might work if the car doesnt bog down, but stock gears and nearly no mods, it most likely will bog (unless you are truly racing on sand, in that case your going to spin). As far as shifting, if your new to it, just make sure you get the car cleanly into gear, at about 5200-5400 on the stock tach. Its wise to get an aftermarket one, but some people do have luk running the car until they feel it start to nose over. I prefer a shift light myself, but everyones different.
For the guy racing new GTs and winning, you seem to have a good deal more mods than the poster, and from what I remember you mention roll races, which are a lot different. An 03 V6 with good driving, and those few mods is a low 15 second car, which isnt far off a stock 5.0. Factor in some things and the race doesnt sound too off. Get better at driving the 5.0 and you have a good chanceof taking him by more cars.
As far as street slicks go, there are tons of tires out there, Drag Radials, ET Streets (what I assume you mean by street slicks) and straight up slicks. Within these tires there are many different companys that make good and bad versions of each. Just list what brand tire you have, and it will dispell all myths. I personally used to run 26x10.5 ET Streets at the track, then went to 26x9 Hoosier Slicks. Now I have some 17" 26x11.5 ET Streets for track use. My Street tires were 245/45/17 Falkens!