New bike - shifting

Well I got my new bike UPS today and assembled it. Everything seems
fine except some derailer adjustments I think I need to make. The bike
has shimano shifter/brakes in one unit. To shift you either twist the
brake lever and to shift in the other direction you push a button
beside the lever down. The problem i'm having is that it seems to take
a bit of time to shift. I make one large shift of the lever and it
changes gears but starts grinding or clicking, until I fiddle around
with a few half-shifts (trim shifts I think it's called) and then it's
fine. The chain isn't at an extreme angle, the noise comes from the
rear gears. Is this normal and something I will have to get used to or
is there a way to make the shifting smoother and quicker? Thanks.