The bowl in which you beat the whites should be large enough to accommodate an eightfold expansion of their volume. It’s often recommended that the cook avoid making egg foams in plastic bowls, because plastics are hydrocarbon relatives of fats, and tend to retain traces of fats and soaps. While this is true, the bowl is also unlikely to release such traces into a mass of egg white. Ordinary cleaning is adequate to make a plastic bowl suitable for foaming eggs.
If you’re beating by hand, a large “balloon whisk” aerates a greater volume of the egg whites at a time and will speed your work. If you have a choice of machines, a stand mixer whose beater both spins on its shaft and traces a curlicue path from the center to the edge of the bowl (a “hypocycloidal” or planetary motion) beats the whites more evenly and leaves less unfoamed. Less efficient beaters produce a denser texture.