The above link suggests the royals want Alex Gordon to be their 3 hitter, using this lineup. While it's much better than the previous lineup suggestion which had Gload hitting 3 (I can't find the link on the team site but there was a story early in spring training about it), I still have my own preference for a few reasons.
The site's lineup projection:
SS Pena, Jr.
This lineup's benefits: It protects Gordon, who needs pitches to hit due to his strikeout tendencies. It also puts Teahen in a spot to drive-in runs after several productive hitters, while not relying too much on his power increase.
Its weaknesses: The 3 hole is usually for a team's BEST all around hitter, which in our case is likely Butler. Also, it burdens Guillen w/ the clean-up role, as opposed to the 5 spot/RBI man hole he filled in Seattle. But perhaps the biggest weakness is that it creates a RR/LL in the 4-7 spots. While we're not in the NL where matchups are more important, this could be a problem in later innings, w/ out machines Buck (admittedly a better hitter against lefties) and Pena following the bunch.
Benefits: Good R/L balance throughout. Allows power production of catchers to be meaningful. Puts Gload in a contact spot, perhaps his best asset. Has our BEST hitter in the 3 hole, an emerging power hitter in the 4 hole w/ protection of a legitimate power/RBI guy in the 5 hole. Gordon can only thrive when people will give him better pitches to hit. In the bottom of the order last year, there was no incentive to throw him strikes. I also like Teahen in the 6 spot, which usually is a contact spot, but Teahen, despite his strikeouts, is a run producer, much moreso than Gload or others that could fill the spot.
Weaknesses: I understand the reasons why we have Buck batting 8th. But too often last year no one was on base when he hit home runs, through no fault of his own. I perceive the benefit of having that power increase run production and eliminating a LL in the 6/7 hole to be greater than the benefit of having a better contact hitter in Gload take the 7 spot. As for the 3/4/5 criticisms, it all seems to come from how you view the 3 and 4 hitters.
All in all, the discussion around lineups is pretty futile anyway. Injuries and suspensions leave us w/ dozens of lineups during the season anyway. As Hillman has said, speculating about it is sort of childish. But, like a child would, I can only dream of the lineup that makes the most sense to me.