Should I get a thin, flat bottomed wok to stir fry large amounts of veggies on an electric stove?

I'll try address your questions:

• Firstly, woks should always be thin. The point of a wok is to get extremely hot at the bottom, without heat being conducted much up the sides. Thin is best for this
• The problem with this in your case, is that a small amount of your vegetables will be touching the bottom and cooking, while most will be sitting on top, or in contact with the sides, just getting warmed slightly.
• The point of a stir fry is to slightly char the vegetables as they get tossed around the pan, moving between hot and cooler parts, so that they cook evenly, but get a good browning at the same time. The problem is that this is really only suited to smallish amounts of food, unless you have an enormous wok and burner/stove.
• As you have indiciated that convenience is more important to you than flavour/cooking quality, I would suggest a large, flat, heavy bottomed frying pan (fine with straight or curved sides). This will cook large amounts of veg best, without cooling down too much when you add them, and the larger bottom surface will mean more veg is getting contact with the hottest surface

I wouldn't normally recommend a plain frying pan for stir fries, but I think this is the best option in your case. The outcome will not be the same as a stir fry - might be more moist and less browned, but should suffice for convenience's sake

There are several different choices you could make which would deliver a similar result:

1. flat bottomed wok: woks have high sides, however the heat is only on the bottom, you need to stir the food in woks very often to ensure even cooking
2. saute pan: basically a frying pan with higher sides, the heat is distributed across the pan but hottest in the center
3. casserole dish: this is more of a pot than a frying pan, usually thick and often cast iron. It takes longer to heat up but the heat is generally very even. A benefit of these is that they can go into the oven, giving you more flexibility

I have all of these and I use them regularly, any of them will work for cooking large quantities of vegetables (provided you get one that's big enough). It's a matter of picking the one that suits your personal cooking style. If you are looking for something that takes less stirring then a wok is not for you.

As for materials it really is a matter of opinion. If you are a lazy cook or just busy a non-stick stainless or aluminum pan or wok heats up pretty quick and is easy to clean up afterwards, however if you tend to burn things you'll destroy your pan quickly in which case ceramic coated cast iron, plain cast iron or steel might be the way to go.

It sounds like a non-stick high-sided saute pan would be a good way to go, just keep the heat under control and don't be afraid to add a bit of water to the bottom to keep things from burning.

Look at the size of your hob, it is probably up to 24 cm. Imagine putting a straight-sided pan on it and filling it 1.5 - 2 cm deep with cut vegetables (the pieces don't have to be exactly a single layer, they can overlap slightly, but the number of pieces not touching the pan should be minimal). This is the maximum amount of vegetables you can stir-fry at once, no matter what your cooking vessel looks like or how it is called.

If you are OK with this amount and your pan is for some reason too small to use it that way, you can get a larger pan (preferably not straight-sided) or a wok, whichever you prefer.

If this amount is too small for you, you cannot stir fry. You could just throw your large amount of vegetables in a higher-sided pan or a small pot, and braise them. This might meet your criteria for "high volume" and "not interested in flavor" (It's not that braised vegetables taste bad, they just have a different flavor). Stirring convenience is unimportant, because you only have to give a small stir once every few minutes. A thicker walled vessel is better for braising (and for almost all types of hot cooking). So a wok won't make much sense.

The third thing you can do is to turn on two hobs at once and stir fry two batches. It will require more coordination, and you can't really do it as true wokking (one wok requires your constant attention), but you can have your large volume done quickly.