All pump systems require a pressure tank downstream of the pump.
How large a pressure tank you need depends on how much water you might draw at one time and whether the supply can keep up with the pump over a long period of time. It is undesirable for your pump to draw water so fast that your neighbor loses all pressure.
Method 1 would use a pump with a fairly low gallons per minute rating (to avoid cutting off your neighbor) and a large, say 100 plus gallon, pressure tank that doubles as a storage tank. You would be able to draw a reasonable amount of water, enough for more than one shower or a full washing machine cycle, while the pump refills the tank at its leisure. The tank capacity should be more than twice the amount of water you are likely to draw at one time. To be able to draw half the tank's capacity, you calibrate the tank pressure to (and you must find acceptable for usage) half the pump turn off pressure even though the pump turn on pressure might not be that low.
Method 2 uses a nonpressurized tank (cistern) upstream of the pump as well as the pressure tank (need not be more than 20 gallons now) downstream. The cistern is filled using just the pressure from the supply line and can use a float similar to that in a toilet tank to turn the incoming water on and off. The pump can be of relatively high gallons per minute rating.
Because a cistern requires drawing in makeup air from the atmosphere, you may need additional chlorination or other treatment at your house and a way to keep bugs out.