Well, assuming you get five chances to choose a song, you're most likely to encounter your own five favourite old time tunes. (And guess what? Other people probably know most of them too, so you won't feel like you're soloing when you do them.)

I'd say, don't worry too much about the first time. Don't worry about impressing anyone. Nobody will care too much if you mess up your own songs. After eight years and well over 500 song circles and music circles, I never take the time to form strong opinions about anyone who hasn't shown up at least three times. Watch others to try to figure out how enthusiatically to join in -- usually the only rules are, don't be louder than the people who are leading songs and don't lose the rhythm -- support but don't interfere.

If I had to prepare five "well known" "old time" songs to sing with a group, I'd choose: hmmm...

Wild Mountain Thyme
Red River Valley
Home on the Range
Waltzing Matilda (well, it's got an "old" sound)
Oh, Susanna

Everyone knows Amazing Grace, but don't try it unless you can already do it. But I'd be darn surprised to have even three of these songs sung at any one gathering.