the wifi uses less battery than the 3g radio and depending on isp, it should provide you higher bandwidth than vzw.
you would want to use it whenever you are in range of a wireless router.
yes there is a wifi widget you can place on your homescreen(press and hold any part of a empty home screen, choose widgets, choose wifi. whenever you use a wireless router for the first time, you will have to go into settings>wireless networks>wifi settings to connect your phone to the wifi router.
after the initial setup, it should connect automatically from your home screen widget. hope that helps. any questions, just ask
for future reference, there is a app called switchpro widget (by alei) than combines alot of switches into 1 widget. try it, im pretty sure you will like it