The Indians have at least one thing to be thankful for this off-season and it is that their list of needs is going to be much shorter than last years. There may be more free agents leaving, but many are inconsequential and those staying are of higher quality than the players remaining after 2012 (even if they are the same players). For the sake of this discussion, we will assume that all free agents and players with options will be let go, while most players still in arbitration or under contract will remain. This means that no trades are expected, even though some are expected, just because they are impossible to predict. Refer back to "Who Will Stay & Who Will Go" for a player-by-player list of the Indians contract situations.
The Indians are without a DH going into 2014, but they haven't had one since Mark Reynolds was released mid-season and it certainly didn't hurt them down the line. Not having an official DH has made the team much more versatile, allowing Yan Gomes and Ryan Raburn to get into a lot more games. With both Nick Swisher and Carlos Santana being liabilities in the field, it may be a good idea to essentially platoon them at first (and use Santana as a part time catcher) and DH. This would also allow the Indians to keep Drew Stubbs in the lineup on a more regular basis, which would severely help the defense.
If the Indians decide to forgo defense and continue to play Swisher in the outfield or Santana at catcher, they could use this hole to add another big time slugger. Of course, any player added would have to be significantly better offensively than either Gomes or Stubbs, who they would be replacing in the lineup. There are actually a few good options this off-season, both in the free agent market and available for trade. An interesting route to go would be similar to signing Giambi last off-season, but any of these players would be a big upgrade. Paul Konerko, Kendrys Morales, Raul Ibanez and Justin Morneau are all former superstars who have become defensive liabilities in recent years. Any would be an upgrade over Stubbs and could probably be found fairly cheaply, considering their career numbers. This means they could be let go during the season with little repercussions (as Reynolds was) if things don't work out.
There is a huge list of other free agents as well, any of which could be used as a DH, but those listed are among the best options as the plethora of options for other teams may drive their prices down. While the big money revolves around players like Shin-Soo Choo, Curtis Granderson and Robinson Cano, the Indians may be able to sneak in and grab one of those other veterans.
Outside of those, there is one trade option that seems really interesting at the moment. The Royals are tired of Billy Butler being a negative in the field and striking out 100 times a year. He has been listed as tradeable and while inner-divisional trades are rare, this one could possibly happen. The Indians farm system is jammed full of second base and short stop prospects, many of whom are within a year the Majors and all of whom are better than the Royals internal options. Giovanny Urshela, Ronny Rodriguez and Justin Toole are about to get even further buried in the depth chart as Joe Wendle and Francisco Lindor advance. Between Kipnis and Wendle, the Indians should be set with second basemen through about 2025, so any second basemen between the two should be considered available. Butler would be a good fit as DH for almost any team, with a .823 OPS and has averaged more than 20 home runs and 90 RBI over the past three seasons, something no current Indian can claim. Butler is owed $8M for next season and $12.5M for the following (in an option) so the Indians would have to weigh that as well.
Finally, there is an interesting free agent out there that is surrounded by question marks. Former Indian Jhonny Peralta has hit the end of his three year deal with Detroit and will be available on the free market. With his main antagonist, Eric Wedge, no longer involved with the team, he may be interested in returning, although the change in position could bother him. He looks to be out in Detroit as Jose Iglasius has taken his position while he was on suspension for performance enhancing drugs. Offensively, Peralta has been remarkably consistent, sitting within .070 of his career .755 OPS in every season since 2006. This means he will likely be expecting a small raise over his $6M made in 2013, but can't expect the kind of contract that even Morales or Konerko could possibly get.
On the Indians side, Peralta would be a solid offensive player who could still play in the field, unlike most of the players listed and Giambi. While Peralta did have an issue playing third under Wedge, he may be more willing to do so under a proven manager like Terry Francona and could be the best available back-up for Lonnie Chisenhall. While it isn't time to give up on the former top prospect yet, a similar situation to this September could occur next year if the Indians are in the play-off race and Chisenhall is underperforming. With Peralta available, he could become the starting third baseman, allowing the Indians to back to the line-up that has Gomes starting at catcher and Santana as DH.
The players listed above are essentially in order of least to greatest for the Indians, but any would be an offensive improvement over last year. There are so many average to great players available one way or another that it would be irresponsible for the Indians to use Giambi as the starting DH or to try to go with the limited internal options. While it is essentially the least important offensive position, having a strong DH can add a new dimension to the lineup when used properly. The Indians just need the proper player to fill it.