Physically you want to go on court already with a light sweat on, so skipping is great as it raises the heart rate quickly and will help wake up your coordination and footwork! Then dynamic stretching (plenty of sites on t'internet with routines etc), maybe a few static strecthes, PNF or SMR depending on how well you know your body. For example, I know my hamstrings are always tight as is my lower back, so after a dynamic warmup I PNF stretch my hamstrings and hip flexors and then SMR (foam roll) calves, hamstrings and IT band.
The I feel lose as anything. After the game, stretch again (more static/PNF) and i'll SMR again to reduce any knots and latic buildup.
Lots of stuff on stretching at www.(the)stretchinginstitute.net
. brackets are because I can't remember if the address has "the" in it!!!
Also, don't get into the habit of thinking of your self as a slow starter. Develop a good pre-match mental routine so you go out convinced you're the faster starter - a la Rafa!!!