Shallow Well Pump check valve location(s)

[RayTu]

I am installing a new shallow well pump and pressure tank. The tank tee I bought came with a check valve and shows it installed before the tank tee with the pressure switch mounted after the check valve on top of the Tee. I did the install, but left the pressure switch on the pump cast iron casing. That caused the pressure switch to chatter / bounce when reaching cut off pressure. So this lead to more research and some confusion. I can move the pressure switch to the top of the Tee which I believe will fix the chatter / bounce issue. The research showed mixed information about the location of a check valve: “Install the check valve: Place the check valve in the piping system between the well pump and the pressure tank.” Or “A check valve should never be installed between the pump and the tank.” Yikes; the more research the more conflicting information about this subject. From the information on this forum I think I should eliminate the Check Valve between the pump and tank and just rely on the foot valve at the beginning of the suction pipe. Is that the best solution? Why is there so much conflicting information about the check valve location? ( Wayne sws100 pump with Flecon tank. Old pump was a Sta-rite with a Con-Aire tank)