I find two of the current TJ two-buck chucks worth recommending. They are the 2001 Cabernet Sauvignon and the 2003 Shiraz. No, they aren't great wine by any means, but they are worth the price. And that is rare for the line from my experience.
The 2003 Shiraz is the better of the two. It actually has a Syrah nose and a bit of a Syrah taste. Good body, too.
The 2001 Cabernet has good body, but is entirely generic red wine. No cabernet flavor.
As to wood?, they come in a cardboard box. These have never seen oak.
Just to be clear, I have not been able to swallow most Charles Shaw wine I've tried. (Yes, I'm a wine snob, and more power to those who always like the entire line.) So in recommending these two I'm saying that for me they are drinkable, and worth the price.
Batches of Two-Buck Chuck change frequently (hence I chose to post to Bay Area board). These were bought at Geary-Masonic branch in SF both last Sunday and today.