The fibre needs to be visually interesting, eye-catching, and that probably means dyed. So that eliminates undyed fibre except perhaps that intense naturally dark BFL I have.
The resulting yarn needs to be good yarn despite containing inconsistencies that creep in while half my attention is given to talking to people. That means nothing I'm planning to make into thin yarn of especially consistent gauge for a particular project.
Since I'll be out in public, I don't want any surprises or difficulty in manipulating the fibre to throw me off or hold me up. That means selecting fibre breeds and preparation types that I've spun before, and spinning types of yarn I've made before. The Icelandic stays home because I plan to try to make a Lopi style yarn out of it, something new to me. The undyed Shetland stays home because ever since I combed it, the fibre doesn't draft as smoothly on the Russian spindle. The Dorset Hampshire cross stays home because I haven't used any yet and don't know how it will go.
There's that lurid superwash BFL I dyed with onion skins then over-dyed with indigo the other week. Would be fun for onlookers to see me spin it fine with large slubs at regular intervals. Because of the colour, it's a showy choice, which is what I want. As an added benefit, when I get the inevitable question, "Did you dye that wool yourself?" for once I could answer, yes.
If I pick the yellow-green BFL fibre, the colour will clash violently with the bright blue DyakCraft spindle I thought about using. A nice bid for people's attention with loud colours, but risks me looking as though I have no artistic sense whatsoever.
Now that I think of it, I prefer to spin in public with a rim-weighted spindle because it needs fewer spins to keep going. Additionally, picking a fibre that's a colour similar to the grass on which we will be spinning in public? An ill-considered choice. You want contrast between your fibre and your background so you can see the drafting zone and manipulate the fibre.
How about a nice bit of humbug BFL dredged up from deep in a forgotten corner of the stash. The swirl of dark and light should be interesting to onlookers and should easy for me to see as I spin. I have lots and it's not earmarked for a project.