If I'm making stew on the stovetop I braise the meat (cut it into generous-sized pieces then brown all sides before adding a 1/2 to 1 inch of stock and let it simmer on low for as long as I can manage to wait before moving to the next steps. You could easily brown on the stovetop and braise in the oven.) Then add vegetables and seasonings and such.

In a crockpot for some reason the order of the meat is counter-intuitive; my (ancient) crockpot instructions say to put the vegetables on the bottom and the meat on top. I usually do a pot roast in the crock pot though, rather than stew.

Stove top stew involves cooking the meat first and sometime during the meat cooking adding chunked up onion. When the meat is close enough to ready then add the cut up potatoes, carrots, parsnips if you like them (I do), and turnip or rutabaga if you like them (I don't much). Sometimes I wait till near the very end and add broccoli florets. The broth usually has some Worcestershire sauce added, some mustard, and I like to add a little red wine. Salt and pepper and a little dried oregano. Whatever broth (chicken or beef) needs to be topped periodically so it doesn't get too thick or sticky. I add a little flour and water mix to the stock right near the end do thicken it.