A very basic question (new at the game):
Let's say you draft a potential major league stud who's 18 years old. How many games of each level of the minors should he play? Does it depend on age/rating? What's the best way to see him reach his full potential? 

You cant really promote a guy too quickly. If he is getting significant playing time, he will develop. You should atleast promote one level per season.

I like at least 1200 AB at a minimum.   400 at three different levels.   Most players get more than that.

Because of DUR/STM issues, I don't have a set number of G/IP for pitchers.  But, if a guy isn't in AAA by his 4th season(when he has to be added to the 40), he's probably not BL-quality.

So Mike, would, say 400 AB at Low A, 400 at AA, and 400 at AAA suffice? Or would you step up level by level? (Rookie, Low A, High A, AA, etc.)

I sort of treat RL/LoA as one and the same.  And I have no problem starting a player in HiA for his half season, leaving him there for his first full season then promoting to AAA and AAA in the next two seasons. 

I've only had a couple of players who were "fast-tracked" to the bigs.   Most get 1500-1800 in the minors with 400-600 at a level.  As I said, I want a player starting in AAA when I have to add him to the 40.  He may have been promoted there the previous season. 

An example:
Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Cesar Mesa   He'll be added to the 40 next season.  While he probably won't make it as a full-time player, he'd get at least 20 games in AAA next season before call-up.

Drafted the same season:
Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Brandon Gray   The plan was for him to get a "September" call-up but I needed him early so he got the fast-track.   Instead of 86 AAA AB, he should have gotten about 400. 

A "normal" example:   Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Rob Gold

Cool, thanks man. 

Mike, what is your target playing time for developing a starting pitcher?

Pitching is different due to the DUR/STM combos.   I do know that my legit prospects are in AAA by their 4th season.   But some are there in their 3rd season.  And some stay there thru their 6th season.  They have different development patterns than position players and there are a lot of moving parts with pitching.   Put 'em with good coaches at appropriate levels and pitch them when they're 100% is the best advice I can offer.

I'd like to add a similar question: I've got a couple kids, 20, 21 years old, who are in AA. They haven't had much minor league experience but they're good enough to start for my BL team. Will promoting them now, after 1-2 seasons in the minors, negatively impact their development? Or as long as they're getting AB's and have good makeup will it all be essentially the same?

Maybe a dumb question but this is my first team.

Playing time, coaching and training are the three most important things in developing players.    You start their arb/FA clock by bringing them up but, if they can help you, they can help you.