Deepest in terms of raw numbers. Rios is a good example. He was a waiver pick last season. I picked up Jermaine Dye off waivers in a competitive 12-team league after the draft last season. Nick Swisher and Michael Cuddyer were waiver picks, too.
Third point- disagree. Outfield, ironically, I would say is one of the SHALLOWEST positions. You definitely do need a top tier OFer, but I would also say your 2nd OF needs to be at least middle tier (ie Del.Young, Rios, Dunn, etc.) By the time you get to the third spot, they are all virutally waiver-wire level players that are easily replaceable, and therefore not very valuable (ie Griffey, Kearns, Teahen, Willingham, etc.)
This goes back to having at least one top-10 player at every position. Nathan, Rodriguez, Ryan, Rivera, Wagner, Papelbon, and Putz are all worth getting early. You need at least one good closer so you're not scrounging for guys like Soria or Owens as your top option.
Unless you get a top 5 closer relatively early (Nathan, Papelbon, Rivera, Wagner or Hoffman)- WAIT! Every other closer has virtually no job security, and this is always the best postion to exploit on the waiver wire. Let the other fools go after the Wickmans, the Borowskis, and the Saitos of the world in the mid rounds, the savvy gm will pick up the Wheelers, the Sorias, the Owens and the Sorianos off the wire, and adhere to other needs earlier in the draft.