I can only give you my personal opinion as a participant and audience member, of course. Above all, remember why you’re there—why everyone’s there. To drink and sing. Not to listen. They’re listening to you while they’re waiting their turn, and vice versa. So it’s only polite to try to provide a little entertainment. There’s two extremes, there’s “I love this song but he/she’s AWFUL” and “I don’t know this song at all and he/she’s AWFUL”. The former is at least cringe-inducingly entertaining. The latter is just bad.
People like to sing along, especially after a few drinks, so something nostalgically popular will probably get them going, whether you’re nailing it or not, ie. songs off of Pearl Jam’s first album. There was a cute, petite girl with little pigtails and without a mighty baritone doing “Jeremy” a few nights ago. She didn’t have Vedder Thunder but we didn’t much care and could barely hear her over our own bellowing. Being continually half a measure off through the entirety of “Dear Prudence” though…no one’s gonna sing along, just groan and laugh. I’ve mentioned the great Bad and Obvious elsewhere: Johnny Cash’s “Folsom Prison Blues” and “I Touch Myself”/”These Boots Are Made For Walking” are the respective gender standards. The men tend to mutter and wander, or drunkenly shout, and the women tend to be acting (and presumably feeling) “sexy” and then pop that balloon with miserably underpowered singing.
If one is going to do “Bohemian Rhapsody” or “Under Pressure” then one should be great. They’re not the biggest clichés but you don’t often get a real tour de force.
The bottom line is that it’s better for everyone present if you sing something you can sing, something you’ve checked on before showing up or previously sung in some other situation. Sometimes the bar is set so low that blowing everyone off the stage is pretty damn easy. If you do that with a song they don’t know and love, well…at least you know you gave them quality. If they do know it, you’re a friggin hero, especially if it’s something not everybody else is doing. But whatever you choose, choose something you can put some oomph behind. On key but meek but can be a little hard to sit through too. And I don’t recommend, or at least don’t particularly enjoy, radical reinterpretations. This one guy did “Creep” and it sounded like Henry Rollins was covering it. Sing it the way people know it, because that’s why you and they like it!
And you’ll definitely hit a wall sometimes. I’m awful with “Mayor of Simpleton”. I love that song but tried it once and it just didn’t work. I can’t sing it like Andy and don’t know how else to do it. Boo!