A jet pump with a foot valve would work, but a submersible in the cistern would be better. A sub will give twice the flow and pressure for the horsepower, and a sub won’t lose and doesn’t have to be primed. With the jet pump a foot valve is all you need, and doesn’t need an extra check valve.
A 50 gallon pressure tank only holds about 12 gallons of water. Even with an 80 gallon tank your pump will still cycle a lot. All you need is a 4.4 gallon tank like the one in the picture to the left, if you use it with a Cycle Stop Valve. The CSV and 4.4 gallon tank will do a much better job that an 80 gallon tank without a CSV. The CSV will also deliver constant pressure to the house instead of constantly varying pressure as with the old pressure tank only systems. I would also recommend a 40/60 pressure switch setting. You will like the 40/60 pressure much better than 30/50.