I can't give you a final recommendation, but I can share a few thoughts on the subject. Given that /etc is usually rather small, you might just go for a simple compressed tar-ball solution. If you hardly need to go through the history, it might be the easiest solution to set up.
For me it would be to tedious to manage logical volumes just to do keep track of /etc and especially as I don't think that LVM snapshots were designed to be created regularly as means for backup of a relatively small amount of data.
btrfs seems to me to be far better equip for this, but it is still not as stable as, for example, ext{2,3,4} and the fsck tool is also not done yet. But it continuously gets better.
Personally I actually use git to track /etc but you should keep in mind that git doesn't store file metainformation like ownership or permission! And also check that the .git directory has the right permission. There are a few tools that help with these problems though. You might want to take a look at etc-keeper, which was developed exactly for the keeping track of /etc or use at least use something like gitperms or metastore to track the metainformation.