I was wondering if I take the shot about 3weeks after the first day of my period will it be effective and if so how long do I have to wait before my husband and I can have intercourse

If you take the shot within the first 7 days after your period you are protected immediately.Otherwise, you'll need a backup birth control (condom) for the first week after your shot.

Source:Depo-Provera - Birth Control Shot (http://www.plannedparenthood.org/health-topics/birth-control/birth-control-shot-depo-provera-4242.htm)