Well, figuring that you're going to get 150-200 IP out of each starter (hopefully), and around 75 IP for each reliever, you can get an idea of what you'll need to reach that minimum.
I'd probably end up drafting six SP, three closers, and 2-3 MRs if the draft went the way I wanted it.
As the season progresses you're basically forced to start your top 4 pitchers for all of their starts, and use your 5/6 guys sparingly based on matchups. After the ASB you'll have to judge whether you need another starter (and to start using them all the time), or if you can even back off on your 4th starter's good matchups.
With only starting your best four pitchers consistantly, along with two good closers and one suspect one, and with two really good MR guys (who could turn into closers), your ERA/WHIP numbers should be looking very good when compared to those starting a five or six man rotation. Your saves should be up there, and the Ks should be looking good as well. The only number you'll be struggling with would be Wins, so I'd focus my #4/5/6 starters on guys who's ratios may not be sterling, but can rack up wins (3rd and 4th starters on playoff-bound teams).
Of course, you could go the other way, grabbing two top-tier closers and 7-8 SP, racking up the W/K/S and hoping to finish in the middle of the pack in ERA/WHIP, but that feels a lot more robotic to me. I like to be able to keep my options open through the year and massage a best-fit for all my pitching stats based on matchups and such. I hate starting a ton of guys just to pile up counting stats... it just feels dirty.
My ideal staff in a league like this would look like (draft-round in a 10/12 team league)
1.) Sabathia/Webb/Beckett (6/5)
2.) Verlander/Hamels/Kazmir/Bedard/Haren (9/8)
3.) Oswalt/Zambrano/Harang/Young (10/9)
4.) Chien-Ming Wang (15/13)
5.) Bonderman/Francis (17/15)
6.) Pettite/Blanton (21/18)
1.) Saito/Wagner (9/8)
2.) Jenks/Hoffman (10/9)
3.) Gagne/Howry (or possibly Borowski/Todd Jones if I thought I needed more Saves) (20/16)
1.) Betancourt (24/20)
2.) Broxton/Bell (24/21)
3.) Okajima/Wood/Accardo/Shields (last pick)
This does require quite a bit of draft-pick investment in the 6-11th rounds, so you'd have to make sacrifices somewhere (probably in your #2 Starter and Closer) in order to keep a competitive hitting team, as that should take precedence over your pitching anyway. But, with the right league, you could definitely pull off a staff like this and still have plenty of studs and prospects to choose from.