If all you're running is the sprinklers, you do not need a pressure tank or a pressure switch and I would recommend not having one. I'd use a centrifugal pump or a jet pump and match the sprinklers to the pressure and volume of the pump.
It would be best if you can get the pressure/volume chart on your pump. But, if not, you can draw an approximation just from the max volume and max pressure it will produce. As long as the pump is a variety of centrifugal, you'll be fine. If you chose a positive displacement like a piston pump, then you have to have other piping in the line as well.
Note: the reason for a centrifugal pump is that you can dead head it without damaging it AS LONG AS it is not overheated. Submersibles typically require water flow for their cooling. Ones sitting on the surface typically use air for cooling.