That 1/8 twist should do very well for the 140 and heavier bullets. It may be to quick for the 120s though.
The 6.5-06 is a fussy cartridge. It is prone to a few problems but once you've figured out the loads it likes you will be very happy with it. I have two of them. One has a 1-12 twist and in my opinion was a mistake to build. It is only accurate with 120 and lighter bullets. Even then, it has issues with 120 boat tails. They have to be driven quite fast to stabilise. There is also the problem with reamers. Most of the reamers that are commonly available have long throats for the 140-160 bullets, not exactly conducive to accuracy with shorter bullets. The other has a 1-10 twist rate and shoots extremely well with 140 flat base bullets. Boat tail 140s won't stabilise in my rifle. The 140s in the 1-10 twist rifle must be pushed at near maximum pressures to get the best accuracy as well. If it didn't have a very tight chamber and neck, there might be issues.
Your 1-8 twist should be fine with the heavier bullets but probably won't like the lighter 95-120 grain bullets. You never know though, you may be lucky and it will shoot all of them acceptably