Getting a student visa takes about 3 to 5 days, and valid from the day it is stamped in your passport. You have no reason to worry at this stage.
I don't know the details, but I've heard it's possible to switch schools WHILE YOU ARE on an F-1 or J-1 visa. What you may be able to do is apply for a visa for your second-choice school, then convert it to a visa for your first-choice school in case you are accepted off the waitlist.I don't know whether this would in fact be faster or not, but it may be worth investigating.