Soak the chopped onion in a small dish of cold water while you prepare the rest of the salad ingredients (this cuts their sharpness while retaining the onion flavour).
Combine the rest of the ingredients except for the avocado, lime juice and pepper in a large bowl. Drain and add the onion. Toss together, then dress with Lime and Garlic Vinaigrette (recipe below). Taste and adjust the seasonings to suit your taste.
Gently toss the avocado slices with the lime juice and a grinding of black pepper. Set aside until ready to garnish the plated salads.
A note about the avocado: I slice it, toss it in lime juice and a bit of black pepper and serve it on the side with the salad. You could cut the slices into thirds and stir them into the salad, but I simply like the look of them better beside the salad.
If you don't have cilantro, you could substitute a handful of chives and 4 or 5 mint leaves, all finely chopped.