No one can really tell you about a specific brand of birth control and its side effects because everyone will be affected differently. Side effects of birth control pills in general are:breast tenderness, diahrea (sp?), constipation, weight loss or weight gain, headaches, dizziness, nausea...And then some more serious ones are numbness or tingling in the arms or legs, or leg cramps. Those side effects require immediate medical attention as it could be blood clots from the pill.
The trick is to find a pill that give you minimal or no side effects. Try this one that the doctor gave you and as long as you get no horrible side effects, then stay on it at least the three months to see how it works for you. If it works then stay on it, if you are getting side effects that you don't like then tell your doctor and he/she will switch your pills.
Some people say that in 7-10 days of taking the pill you are protected to its full ability. Others say two weeks, one month, but my doctor always told me three months. That is when the pill is at its full affectiveness.
But, the bottom line is, if you don't want children then you also need to use condoms. Birth control is only 99% effective if taken 100% correctly. All sorts of things can counteract it and having unprotected sex is just asking to get pregnant.
I am so sorry about your miscarriage. I wish you the best and if you need anyone to talk to, just pm me.