^^Yes to Sheila's response. See if this link might also help..

https://www.thekitchn.com/how-to-whip-egg-whites-make-me-139505s

Bowl size for small, medium and large can vary greatly. You might find a set of small, medium and large bowls that range around 2, 3 and 5 quarts.

For what size bowl to use, this might help.

"Use a stainless steel or glass bowl. Plastic bowls can retain a film of grease. Bowl size (and shape) matters. For proper aeration, a small mixer bowl is best for up to 3 egg whites; a large mixer bowl for 4 or more egg whites. When beaten, egg whites increase as much as 6 to 8 times in volume. The bowl should be large enough to hold the expanding whites, but not so large that the whites are spread too thin. The bowl should be deep enough for the beaters to make contact with as much of the whites as possible."

And I always wash my bowl AGAIN before I do the egg whites -- I want to make sure there is nothing in the bowl! I have a copper mixing bowl that I use for egg whites and it seems to do a better job than my stainless steel one.

It is sometimes hard to get all the sugar to dissolve properly. Look for a recipe that uses both granulated sugar that you gradually beat into the whites, beat until shiny and stiff, and then has you fold in some powdered sugar. This Rose Levy Beranbaum recipe worked well. You could leave out the chocolate but it was a nice offset to the sweetness. I chose to add some instant espresso powder as well.

https://www.fodmapeveryday.com/recipes/chocolate-spangled-meringue-kisses/

Another way to approach the sugar is to measure it then run it through the food processor. With a stand mixer, it wouldn't be a problem.

Even though a couple of generations ago, it was standard to whip eggwhites on a plate with a fork, I like a deeper than wider bowl. That gives them something to climb up, though the hand mixer is a hindrance and will demand a somewhat shallower bowl. I can completely inflate a dozen eggwhites from size large eggs in a five quart bowl. For fewer, I'd still go with a big bowl, especially if it's not too wide, to give yourself room to maneuver. I've tried a hand mixer and didn't think it did a good job, so before I had a stand mixer, I just whipped them by hand with a fork or whisk.

I don't have any issues with a stainless bowl (Martha's copper is classic, but I don't have one). The problem would be a bowl that's too slick. I wouldn't try glazed ceramic, and only glass if it's been beaten in before and roughed up a bit. There's a subtle texture to unpolished metal that helps the egg cling and climb.

The reason to start slowly is so you won't be decorating the kitchen with egg slop. The actual aeration would be on high. You'll eventually get there at any speed, but why work that hard?

Length of time to stiff peaks is quite variable depending on your equipment, eggs and number of eggs. I once did a dozen by hand and it must have taken at least 20 minutes. I should have done it four at a time. The best I can say, since you're probably using a dozen for meringue cookies, is that it'll take longer than you think it ought to, but not nearly as long as it could. :)

• Don't overbeat or underbeat. Not flopping over doesn't mean truly stiff. There would be a thin peak when you pull the beater away, and it should stand at attention type stiff. The meringue should be glossy not floppy. If you overbeat it'll start to liquify again and should become a nice omelette.
• Always use a scraper to turn the bottom once or twice (without squishing) to make sure there isn't a pool of unwhipped white.
• If your recipe has any salt in it, but 1/4 tsp, or however much called for if it's less, into the eggwhites. It helps them retain their loft.
• For meringue cookies, piping usually works best. If you don't have a piping bag you can use the ziploc with a corner cut out method. Before you start your recipe, get your bag ready and find a vessel to use to hold it while you're filling. It might be a wide pickle jar or coffee can or similar sized vessel. Something tall enough that it'll hold the whole working part of the bag without touching bottom. Fold the sides of the bag over the vessel. This makes it a lot easier to fill without squishing the eggs.
• YMMV but I like plain old fashioned matte but not textured aluminum baking sheets, no paper. I think th paper keeps too much of the moisture.

Before you bake, you should also decide what texture you like. Some prefer crisp outside and chewy in the middle. I prefer crisp all the way through. As far as I know, the only difference is how long you bake it. I don't know a good doneness test but the chewy ones feel heavier in the hand (the weight of the water that makes them chewy). You can compare recipes to get an idea of timing.

Have fun! Meringues are magic. :)

Best to have egg whites, bowl and tools at room temp. or warmer, for more volume, I believe...?

And the recipe I use has cream of tartar - 1/4 tsp. per 3- 4 whites.

A dozen egg whites for meringue cookies? Unless she’s feeding a huge crowd I would think three would be enough.

Beat egg whites to stiff peaks with a fork on a plate?? My grand mother would beat whole eggs for scrambled eggs that way....but a hand cranked egg beater was the tool for meringue.
And my recipe that makes 5 dozen cookies used 3 egg whites.
Oh....and neither my mother my mother in law nor my grandmother owned anything but crockery bowls and their meringues were just fine. I think the myth of havign something to climb only is important for an angelfood cake

Just my personal experience, Linda. I imagine your m-i-l's and grandmother's crockery bowls weren't as slick as mine. I can (have) even get high volume stiff peaks in Tupperware. Anything can work. A taller and less wide metal bowl gives me the best volume with the least effort. And the Tupperware does have some texture. I find too smooth a bowl hard to get it going in.

And, yes, I've seen the eggwhites done with a fork on a plate. I was flabbergasted, but it worked.

Sorry about the proportions being off. I forget that most people's idea of a cookie recipe has a yield of one dozen. :) A dozen eggs will get you 3-4 dozen depending on the size.

I make fairly good sized meringues for my MIL; 3 egg whites usually yields at least 18. If I made them one bite size I’d probably have more like 5 dozen.

FWIW, both Jacques Pepin recommended using a copper bowl and balloon whisk for egg whites. Something about the copper reacting with the egg whites?