This list is volatile, to say the least, but here's a basic idea of the tunes we play here. Don't put a ton of effort into learning all of them, we might do some, we might do none, it depends; point is, they all are dirt basic and should take like 10 seconds to learn on the fly. (that's the idea here). But this list should get you in the ballpark of what target we're shooting at.
Can I sing/play a song?
Sure - but keep it in the ballpark we're playing in here, and keep in mind; it has to be easy enough that you can explain it in 2 sentences, ie "I IV V in A" , "verse is C , chorus is G and F", and people will understand it without knowing the song. Picking one everyone is at least vaugely familiar with is a smart idea. That type of thing. If you have to explain it - "in the middle it modulates to Bb harmonic minor and is in 7/8, until the 18th bar which is a bar of 11 and goes to Cm7b13#22bb69" etc, them it's not a good candidate for this situation. (PROTIP : I often leave out bridges that modulate/go all over the place, in the interest of keeping things cohesive.) Again, keep the song in the ballpark we're playing in. Read this list, it'll give you an idea of what we're doing here.