Chorus singing certainly can't be relied on these days. I was in my local FC the night John Kelly did Shallow Brown as part of his set. As refrains go, it's not what you could call demanding. Me and one other person joined in. I suspect that anywhere with a stage and chairs in rows is likely to be pretty dead for chorus singing, unless the singer really works the audience (Come on, give it a try - Shallow, oh Shallow Brown...)

I love Jones's Ale, not least because I heard it for the first time at my local singaround, sung (or rather led) by a guy who'd been in the main part of the pub and wandered in. My version is, accordingly, collected from This Bloke Who Wandered In, further processed by being sung all the way home, and updated a bit after googling the next day. I only mention this because it's ended up sounding nothing like the Coppers' version, which I guess has a certain canonicity. People still join in when I do it, though - at least, in places where people do join in.

In terms of verses, personally I sing the Dyer, the Mason (interesting hints of atheism in that verse) and the Soldier, followed on a good night by the Folkie:

Now the last to come in was a folkie
With a voice so wheezy and croaky
And his singing was really in no key
All to join in that jovial crew
And he sang them a song from the days of yore
With some extra words he'd added the day before
It's the living tradition, boys, say no more...