When I brown meat for use in a stew, I cut them into small pieces first. One of the tricks I’ve learned is that 75% of the cooking time is on the first side. Then you flip only when they’re practically cooked through.
This doesn’t apply if you’re browning thicker cuts like a steak or a roast, where you need more or less equal time on each side.
I’ll repeat the advice about NOT moving the meat. Do as little moving as possible. Talking about small pieces, I’d move them twice - once to flip, once to take out of the pan. With a steak, I’ll move it four times - turn, flip, turn, put on a plate.
In terms of the temperature, I heat the pan with the oil in it, and put the meat in right when the oil starts smoking. (And by smoking, I don’t mean much actual smoke, just the first evidence of vapor coming off it.) Depending on your type of oil, that’s 375-450 F; anything above 350 is enough for Maillard reaction that produces the browning. The meat will cool the pan down a little to stop the smoking. Once the meat is in the pan, you don’t want the oil to do any more smoking, so keep the heat down if you need to… but you shouldn’t need to. If oil is still burning, it may be an issue of heat distribution rather than overall temperature. A heavy pan will help there, as others have said.