Updated: Nov 13, 2020
Ideally one should use a purpose built SS milk foaming pitcher for this purpose. There are many excellent ones out there at reasonable cost. A good quality pitcher with good balance is an important tool in any barista's arsenal.
Image: The Eddie milk steaming pitcher by Fellow Corporation USA
However, if for some reason, you do not have access to one, you need to keep two things in mind while choosing an alternate cup/container - its capacity and heat conduction ability. Having a pouring spout is nice to have too but not critical if you are not into precise pouring and/or making latte art.
Why are these two factors important?
The size (or volume) is important, because milk to coffee ratio matters in making nice tasting cappuccinos and lattes consistently. For example, if you are following the 1/thirds recipe to make cappuccinos, which is a third of espresso, milk and foam, and say you choose to heat and foam 120 ml of milk, you should choose a container which is at least double the milk quantity or 240 ml as textured milk will expand up to twice its original volume. A correct cup size will help you to consistently determine correct cold milk quantities, e.g., - half a cup etc.
Heat conductivity of container is important because you can keep touching the outside surface of the container to find out when the milk has reached the optimum temperature of between 65° to 70°C. At this temperature range, you will not be able to touch a steel pitcher more than a few seconds. So a double walled one or a china container will not be ideal because they do not conduct heat rapidly.