FWIW I have a Bergara thumbhole break barrel single shot. I had decided on this as it's affordable, has a good name, it's ambidextrous, and it's .308 (other calibres, quite a few, are available.)
Initially it was simply awful in terms of accuracy. It's a very light rifle and I think some of it may have been down to pilot error and I definitely had to made a significant effort to cancel out a developing flinch. The recoil was not severe in any painful sense of the word, but it was wild. As I was experimenting with loads the group sizes started to shrink just as I was on the cusp of sending it back. A sound moderator calmed the wild recoil down and it is now a manageable rifle that is shooting comfortable within an inch at 110 yards using hand loads. Factory loads are more variable. Apart from the initial accuracy issues, which I cannot account for, the only other criticism I hold is that it would have been nice if it ejected the case when you break the barrel rather than poking the case out just enough to grab it, but a bit of practice makes a reload in reasonable, but not great, time. In all, I like it.