How do you wire up a Square D pressure switch for 115v?

The pressure switch is just a set of N/O (normally open) contacts. The supply voltage doesn't cause the switch to operate. The water pressure does. So, go ahead and land the wires as if it were 240 volt. It isn't required that you break the neutral, but it isn't against the rules. I suspect the switch is rated for UP TO 250 volts.

Your wiring should include a bare wire as a ground or a insulated green wire. You would attach your ground wire at any location along the way that has a place for it. If you don't have a ground then I suspect you have pipe and as a result you can (must) pull a ground in it. Grounding is way more important for something like this than you know.

Most motors (pumps) now come with the ability to swap from 240 - 120 volts. So there should be no difference in that cost. If you get a 120 v pump with the same capacity as a 240 v, the 120 will draw more amps than the 240. HOWEVER, the Cost to Operate each is "exactly the same". Volts x Amps = Watts. And when you double the voltage you halve the amperage. So a 120 v motor that draws 10 amps will use 1200 watts, The same motor at 240 v will only draw 5 amps but still uses 1200 watts. The only part that would be cheaper would be the difference between a single pole and a double pole breaker assuming both called for a minimum circuit of 20 amps.

The feed is a 3 wire system, hot, neutral (return), and a ground. The pump connect the grounds together with a jumper to the terminal for the ground, connect the neutrals together and the hot and the pump hot are switched. If you are unsure about any of this contact a local qualified professional electrician to do the work.