Beyond all the fine advice above, the one thing I remember from Home Ec classes (all those years ago) is that you need to carefully break each egg into a small bowl and make sure that any with broken yokes aren’t used. Once the yolk breaks, there’s a contamination of the white that will ruin the whole batch if you use it. Also, be careful not to put your finger in the whites to retrieve bits of shell…the oils from the fingers are supposed to change make a problem, too.
And if Julia Child (RIP) is to be believed, then you “absolutely must” use chilled copper bowl. Being too poor for that, I’ve always found great success with a good heavy stainless steel mixing bowl that I put in the freezer for about 30 minutes before putting the room temp whites in it.