So far I believe every new champion has been rotated in the week of their release; I will be surprised to see if/when this fails to occur, unless more than 10 champions are released (in some kind of Great Week of Awesome.) Making the new champion free entices people to want them in the future (if they like how the character plays), and perhaps more importantly (except from a marketing standpoint), encourages enough play of the character to ensure a great deal of statistical data for quick balancing following their introduction. I hope that barring unusual circumstances, new characters are always free for a week (I could see keeping them in for their first 2 weeks making sense even.)
Beyond that, I think balance (across roles/types of champions rotated in a given week), variety, and relative uniformity (no champion should go for an exceptionally long time w/o being available relative to others) are all that really matters. While it's true that the free champions of a given week are most likely to be played by those new to the champions, and thus in some cases, more likely to feed, there is no where else for players to learn those champions, so I think the only thing to do here is trust to the matchmaking system to work out reasonable teams more or less, and trust to individuals to make balanced choices of characters within the lobby.