Definitely grab Beckett. He's looked good as of late, and he will give you more strikeouts than Meche.
I'm not a huge Clement fan. I dropped him a couple of months ago, and even though he's had some nice games since then I've never regretted it. He's too unpredictable; he's either golden or completely blows up. Consistency is one of the most valuable traits a pitcher can have for a fantasy manager.
Of the other starters, here's something to consider.
Sabathia's next start is against the Devil Rays (on Friday).
Washburn's next start is against the Tigers (on Saturday).
Both are good spot starts. If you are on Yahoo, you could pick up Sabathia for Friday's game. On Friday you can drop Sabathia (opening up a roster spot on Saturday), and pick up Washburn (again, on Friday). Then you can decide whether to stay the course with Washburn, grab someone else, or spot start the rest of the way. jdh seems to be pretty much on target with his evals...
I'm assuming, of course, that you are not facing any kind of IP crunch.