second gear is a good gear to start in. shifting without the clutch wont hurt anything but you have to let off the gas to do that, you will be faster if you do this.
start the race as normal and hold the gas wide open constantly, never let off the gas until you finish. to shift, keep pressure on the shifter and just tap the clutch for a split second when you are ready to shift. it will slide into the next gear and you never had to let off the throttle. it sounds like a lot to do, but once you do it a couple times it will be second nature and you'll be doing it all the time.