IIRC exos will emerge from one of the two exo-galactic wormholes on the AI homeworlds. You can estimate when they'll arrive based on how fast the % counter increments (though if a reasonably accurate timer could be made, I'd like to have one).
As for size... it's a surprise
But as a rule, the longer the exo takes to charge the bigger it'll be.
My recommendation: just go ahead and see what the exos are like. Learning is a !!FUN!! process, after all.