The best barrel for performance in a 25-06 is a 26" tube.
Trying to keep it a light rifle is difficult with a tube that long.
You could get a light weight sporter barrel or get a heavy barrel and have it heavily fluted (not cosmetic). See
http://www.dtechsuperstore.com/mili%20Guns.htm
The real gain of the 25-06 over the other quarter's is the ability to hold a lot of slow burning powder driving up velocity, this needs a long barrel to take advantage of. unfortunately most commercial rifle makers don't care an 22-24" is the norm in this caliber. Remington did make a 26" Sendero and Savage makes/made a 112 Low Profile in 26"... both are heavy barrel guns.
If I wanted a 25 cal and wanted to keep it light weight, I would look into the 257 Roberts. In a modern rifle you can use +P data. You can get ideal performance out of a 22-24" tube and shooting 100 grain bullets and Win 760 powder you can get identical 25-06 velocity.