Can anyone state how a player that you draft spends his years in your system?  Say in theory a pitcher is drafted:

Say, one year in RL
one year in A
one year in AA
(at this three year mark, is he a minor league FA?)
one year at AAA
Big Leagues....five year mark he is a FA? 

Is there a formula for the progression?  I could be all wrong here, but is there a way to look at a draftee and kind of know how long you can expect to benefit from him before you either have to let him go as a FA or pay him the mega bucks?

Thanks

Players can become minor league free agents after 6 seasons provided they are not on the 40 man roster.  If you add him to the 40, you can keep him indefinitely.

Once he starts accumulating major league service time, it's a different story.  Up through his first three years of major league service, he makes the major league minimum (plus a 5% raise each season).  Then he has up to three seasons of arbitration.  Usually, the first arb season will be fairly inexpensive (between $1m and $2m).  Second and third arb years he will demand more, and if he's really good can start getting expensive at that point.  After six years of major league service, he can become a free agent once his contract exprires.

I like having players progess through the entire minor league system, with some exceptions. At the moment I have a team that's running like a well-oiled machine, so I can afford to let guys mature a little longer in the minors. But when I first started playing my team was a mess, so I had to rush some guys up to the big show. It's all a matter of situation and need.

In general, though, I like to focus on hiring good rookie league coaches and starting guys off there. The major exception with that is that if I sign an IFA long before the RL begins play, I like to start him at Low A so he gets extra playing time in, and I'll just progress him through the system at a normal pace after that.

You will find lots of other owners who like to always start great prospects at Low A or High A. It's a matter of personal preference. I just find that prospects consistently halt or slow development far more often if they reach the majors sooner than they should.

I tend to always start at Rookie and progress one level at a time.  But once they're ready for the bigs, they'll go up.  I have no problems with going diredctly from AA to the majors, skipping AAA totally.

I have noticed a few teams that are well oiled.  You will see guys that are 90% to their projected OVR of 85 (for example) still in AA or something.  The temptation to bring guys up to the BL level is pretty strong, especially if they can help now.  The hardest part is having the patience to build a strong, self replicating farm system and not bringing nearly ready guys to the BL level. 

I am new and would like to try to be patient and progress guys one level at a time (with occasional variations, depending) and have them be very very near their maximum ratings before hitting the show.  Is this the correct way to do it?

Well keep in mind that it's not about when they hit their maximum ratings, it's about when they stop developing. Usually this takes about 5 seasons or so (or at the very least, at the 5 season mark, it slows down so much it's barely noticable). I like to bring guys up once I've seen that during consecutive minor league cycles, they're not progressing anymore. That's typically my cue that I either need to bring them up or trade them.