Jump in is generally OK for a tune session where everyone joins in but for a singaround where everyone joining in (except in choruses) is not the norm, I prefer round the room with an MC who ensures that everyone who wants to sing gets their turn. Even with a session having someone who keeps an eye on things and ensures that everyone who wants to at least has an opportunity to start a tune makes for a better session.

A good singaround has a good mix of solo and chorus songs. One or two who play a tune or recite a poem instead of singing also helps to provide variety.

I think it's important to bear in mind that a singaround is a social occasion. It's about participation rather than performance and it's not a concert. The norm is that everyone who wishes to is given the opportunity to contribute. OK so some are not as good as others but the number of really bad singers/players is very small indeed and I think that those that bang on about them are getting things out of proportion.