Yes, I use Redding the redding 3 die comp set in 25-06. You could get just the standard set, with a .270 bushing.
I use winchester brass and full length size in my die. Next I trim to length (same a 25-06). Deburr the flash hole, and neck. Finally I run it trough the carbide neck sizing die. The brass has been formed for your 6-06 at this point. Add primer, powder and bullet. On the next reload I will clean up the primer pocket and just run it trough the neck die.
This is pretty much the same steps I use for all my reloads along with brass sorting and weighting. It only takes one pass in the neck die (with imperial wax) because it is a very small step down and does not strech the neck out enough to require it to be trimmed again.
It is a great wild cat to begin with because it is so simple and requires no fire forming to create the 6-06 case.
If you wanted to use Lapua 30-06 brass you would need to step down the neck in 2-3 stages with different bushings. I personally do not feel Lapua performs any better in my rifles. It does however shorten brass prep time (no trimming, deburring, weighting, etc)
And I will get a few more reloads out of it, but not enough to make me jump right in buy it when brass like winchester is around.
My .02cents worth based on my experience with my 6mm-06. I use the rifle for PD's, coyotes, deer and antelope and load 70gr NBT, 85gr Speer BTSP, 88gr Berger FBV and 95gr VLD. 1:10 Krieger @ 26". It has done everything I have asked of it. I know there are similar rounds and I went with what was right for me.