Unless you're building a utility package, Chainer's what you're looking for. A big part of reanimator decks is getting around mana costs.
Shirei falls into the list of "package cards", like Sun Titan or Isochron Scepter or Reveillark (if you're not just going straight up combo). These cards are good, but get better if you build around them.
Private Mod Note
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Rollback Post to RevisionRollBack
Card advantage is not the same thing as card draw. Something for 2B cannot be strictly worse than something for BBB or 3BB. If you're taking out Swords to Plowshares for Plummet, you're a fool. Stop doing these things!
Shirei falls into the list of "package cards", like Sun Titan or Isochron Scepter or Reveillark (if you're not just going straight up combo). These cards are good, but get better if you build around them.
On phasing: