There are a lot of good Youtube videos on steaming milk with your espresso machine. For example, these videos by James Hoffmann or Lance Hedrick.
But everything I found, already started with the idea that you already have the proper milk pitcher.
It is really hard to find the answer to the question which size milk pitcher (or pitchers) you should actually buy. As I obviously needed to buy something, I can now answer that question.
I have a 200 ml (7 oz) one, that one is perfect for 1 cup of cappuccino. And I have one of 350 ml (12 oz) that I use when I make 2 cups of cappuccino. Don’t bother with finding one with measurements on the inside: you’ll never use that, as you need to fill it till the start of the spout anyway.
(And yes, I obviously started with the larger one, and found out that it was too large, and I needed another smaller one… :))