YOU can decide. They will push for the soonest possible ship date. Be stern and say I want to leave by xx/xx/xx and/or I do not want to leave before xx/xx/xx. They can say all the things in the world, "you have to go now," for example, but you are ultimately going to decide when YOU go. So, don't feel like you have to do whatever they say when it comes to choices like this. You will have to set on a date before you go to MEPS or at MEPS, I can't remember which.
I had a date of Nov. something and my recruiter pushed me to go sooner in Oct. and I went. I later found out, I did have the choice to remain with my original date, contrary to what my recruiter had me believe.
Also, do not let your college education go to waist, the above poster is completely correct, you should go in as an Officer, not Enlisted.