The actual number of soldiers in the GAR at any point in time is highly unclear and a topic of debate. Writers at the time did not coordinate much on things like the structure of the GAR, designation numbers, and the growing/training process, so different numbers are given by different sources, and often the numbers given do not line up with what we see in the show/movies and seem vaguely implausible. I would recommend reading through the behind the scenes section of the Wookieepedia article on the GAR, as it explains the disparity more thoroughly than I could. Essentially, you may decide for yourself which numbers to go with, though it is a common estimate that there were three million clones in the Army one year after the Battle of Geonosis (21 BBY). Over 200,000 clone troopers were known to be present at the battle, either on the ground or on the ships, and this number is usually assumed to have increased quickly (within six months) to the 1,200,000 quoted by Lama Su.
As numbers are unclear, the rate of production of the clones is also unclear. Supposedly, the Kaminoan cloning process takes ten years to produce one fully grown human, while the Spaarti cloning process takes one year. “Millions” of Spaarti-grown clones were added to the Army towards the end of the war, meaning that Kamino was not the only source. The rate of casualties is unknown, but judging by the existence of the Republic military enhancement bill (21 BBY, authorizing the production of 5 million additional Kaminoan clones), the troops were dying faster than they were being replaced. It is known that the training of the Kaminoan clones was rushed more and more as the war went on. Other than that, very little solid information is available.
I hope that is of some help at least, and sorry I can’t give a more definite answer!
~ Jacen
Links / Before You Ask / Tip Jar