What roles do Progesterone and Estrogen play in your monthly cycle?

What are their purposes and what happens first Prog or Estro?

That question has an extremely complicated answer. I will do the best I can to explain.

Day 1 of the menstrual cycle is the first day you bleed. During this time, a new oocyte (basically an egg) starts to grow and it secretes ESTROGEN. The estrogen begins working to replace the lining of your uterus after you have finished bleeding (around day 5). There is a spike in estrogen due to the oocyte becoming big enough and a few other complicated things that I won't go into (around day 13/14, although it varies woman to woman depending on the length of their cycle). This oocyte continues to grow until a hormone from the pituitary gland (in your brain) causes it to burst out of the ovary. This is ovulation and occurs roughly around the 14th day (again, it varies woman to woman and there is no way to know when it will happen). After ovulation occurs, there is part of the egg left in the ovary called the corpus luteum. This secretes the hormone PROGESTERONE. Progesterone builds up the uterine layer and more or less makes it "fat and squishy" so, if implantation does occur, the baby has a nice environment to grow in. Around day 28 or so, if implantation does not occur, more hormones from the pituitary gland cause the lining to slough off and your period to begin. And then it starts over again.

Also noteworthy, progesterone also begins to thicken the cervical mucus and cause the cilia in the fallopian tube to beat the opposite way to prevent the egg and sperm from meeting, because at this point in the cycle, pregnancy cannot occur anyway (the egg must be fertilized within 24 hours of ovulation).