In my experience with 8 different #1's consisting of A, AB, B, S and V models, the issue of poor accuracy is often over exaggerated. I have been able to find loads that have shot MOA pretty easily. On a couple of occasions, I have lucked into load combinations that have done 0.75 or 0.5 MOA.
Some era's are better than others...red pad era vs black pad era used to be a common delineation mark but some of the new runs also use red pads.
On some of my newer guns, I have found that bedding the front of the fore stock helped with consistency. Most of them have shot fine "as is" from the factory though.
Generally, the triggers are heavier than I like and it is easier to get triggers worked on or replaced with bolt guns than these rifles, but there are options out there.
Do you know what version of the rifle you have in mind? Alex Henry style (A), Standard (B), International (RSI), Varmint (V)...I ask because the two chamberings you mention are common to just a couple of configurations.
The .25-06 is most commonly seen in the standard and varmint configurations...but there are also some AB (light sporter barrel, standard fore stock, no sights) and AH (light sporter barrel, Alex Henry fore stock, no sights) around. The AB and AH are much less common though.
The 6.5x55 had a few runs in the A and RSI configurations. I believe Lipsey's ran both of these several years apart. Not a lot of either made if I remember correctly, but you can still catch them on Gunbroker or elsewhere pretty regularly.
There may be one or two configurations that I am not remembering that hopefully El Numero Uno or one of the other more well versed members can chime in on.
