My comments are strictly from the perspective of a UK singaround or folk club floorspot. I have very little experience of the US-style group sings, which I think probably require a very different approach.

The thing to bear in mind is that those of us who have hundreds of songs we can sing from memory built up this repertoire over a period of years. You don't need a vast repertoire to start singing at a singaround or club - in many cases you'll only get a chance to do two or three songs in an evening. Half-a-dozen songs should be enough to get you started, and then you can keep adding new ones to your repertoire one or two at a time.

It is not a sin to repeat songs, provided you don't do it too often. If it's a good song (and if it isn't, why sing it?) then your audience may actually welcome the chance to hear it again.

There have been a number of suggestions made during this thread of how best to commit songs to memory, and most of them can be summarised as "repetition". Sing along to a recording. Keep singing the song at every opportunity until you can do it without the words. But remember, that's just the start - keep singing the song until it's a part of you.

Someone earlier in the thread made an important distinction between "amateur" and "amateurish". It may be OK in a fairly private setting, whether it's the back room of a pub or folk festival, to accept poor singing or reading from books in the spirit of encouraging participation, and we all have to start somewhere. However in a more public setting (a singaround in the main bar, for example), and especially when people have paid to get in, then both the audience and the music should be entitled to a more accomplished performance.