I believe the CG63 was available converted to 308 but I have never seen one. The fast majority are 6.6x55. Tradex (board sponsor) has several.
Those who like them, like them a lot. I am one of those, but comparing to full out TR rifles, they really can't compete. These were converted military actions with new stocks, barrels and triggers designed in 1963. The world has moved on to better barrels, triggers, stocks etc.
Again I still really like mine. I like TR shooting and plan to try mine out a longer ranges this year. I just have too many other shooting interests to go big and pay for a new TR rig. Based on this, my CG63 works for me to dabble with at distance.
A step up would be the CG80. The best apparently have Shutz and Larson barrels, height adjustable cheek pieces and a rail under the fore arm for attaching a bipod (resting between shots) and hand stop.
One limitation (that may or may not matter to you) is that Swedish target shooting is/was apparently limited to 300 yards. As such, most sights only provide enough elevation for 600 yards. I have a shim for my rear sight that hopefully will give me the right amount of elevation for 1000. Modern target rifles adjust the height of the front sight for major distance changes, so your head maintains the same cheek weld.
The best information I have found on CG63's is the Swedish Military Forum on Gunboards. Lots of members from the states and EU that seem pretty knowledgeable.
As for accuracy, as with all rifles, they vary. When I first got mine it was horrible because the bedding was worn out. Now it shoots not too bad. About 1.25-1.5 inches at 100 yards using 120 Gn bullets. I have not had much luck with the heavier 139's but I am working on a test load using these to see if I can get some better down range performance over 300 yards. We will see.
My friend has a CG 80 the S&L barrel and it shoots closer to 0.5 to 0.75 inches. Kind of makes me want to punch him just a little bit.
As for the need for Peep sights, if you want to shoot without a scope then yes, aperture sights are the way to go. They have been proven to be more accurate and easier to use than open sights. When matched to a circular target they provide a very accurate and repeatable site picture. Select the front aperture (or adjust it if using a front diopter) to provide a ring of light around the black target dot. When sighting, simply maintain the same amount of light on all sides of the target and you are on target to (hopefully) hit the middle. This is what I picked up on the web and from magazines. Others may have different opinions. Again, I only dabble.