Is there a general strategy to cooking a stew?

You can't give a general approach the way you outlined it, as different cuts of meat (and different ages of the animal) demand different cooking times. So the timing of the vegetables would have to be "X minutes before the meat is done"... (and that leaves out the characteristics of your particular batch of vegetables)

Then there's the option of adding a vegetable in two batches, once to add flavour to the stew (added very early in the process) and once just in time to get the vegetable cooked to taste.

So there not really a standard approach, but more a few basic principles to be understood and then applied at will.

(As an aside, flouring the meat is done here in France sometimes. I don't quite agree with the reason given not to flour the meat, as the maillard reaction needs both protein, from the meat juices, and sugars, from the flour. Browning only the flour would be closer to a caramelisation process)

Stew, in it's origin idea is way of creating a meal from oversalted cured meats during winter, long stored vegetables. Those things can vary from time it was stored, temperature it was kept in and amount of salt.

The rule of thumb is "STEW all until it's soft". You put meat and hard vegetables together. Add whole potato to have something to absorb the salt. If using fresh meat you need to fry it on high heat before to keep the moisture inside meat. And that's all. I've never seen a gulasz recipe that had time included.

If you're struggling, one thing you can do is fry the meat (in one or more batches), reserve it in another dish, then fry the vegetables (again in one or more batches). This is normally done to avoid overcrowding the pan but makes the timing more flexible. Then you can add everything back in and stir it up with a little flour before adding the liquid. This is a good time to add garlic as well (if you want it) as it's easy to burn garlic.

Although I cannot compete with all the wonderful chefs above, I can affirm that I make a simple stew in a crockpot and it tastes wonderful! No browning, no flouring of the meat. Just throw everything in and let in cook 6-8 hours on high.

Spray the bottom of the crockpot. Put sliced onions at the bottom. Add 1/4 cup barley or rice (gluten free). desired vegetables (any combination of carrots, potatoes, sweet potatoes, celery, turnip, or other root vegetables). Add stew meat in chunks. Add bay leaves, garlic powder, black pepper, paprika and salt. Add packet of onion soup mix, if desired. Pour in water until it reaches ALMOST the top of the meat, but doesn't cover it. After 6-8 hours, mix thoroughly and enjoy!