The Mariners had a disastrous 2008 season, plagued with injuries and problems behind the plate and at first base. They released Jose Vidro and Richie Sexson last season so Miguel Cairo had plenty of playing time.
My personal preference would be to move Mike Morse to first base, and then you don't have to sign Kevin Millar, Nomar Garciaparra, Lyle Overbay, or Jason Giambi. Then, the Mariners wouldn't have such a clogged outfield. With the possible departure of Raul Ibanez, Miguel Cairo, and Willie Bloomquist, the Mariners would have an extra $8 million to spend.
The Mariners could spend that money on a first baseman, they could get any first baseman on the market who's name is not Mark Teixeira. If they were to trade Ichiro to a team for prospects, that means the Mariners would have over $20 million to spend on players. They could sign Mark Teixeira with that money.
More realistically the Mariners could easily sign Kevin Millar or Lyle Overbay. Both would be good fits for Seattle and it wouldn't blow their budget.