My understanding is that I need a 1 phase(household) to three phase converter to do this.
Yes. Usually these are used if you need to control the speed, torque, or another aspect of the motor. If you just need a constant 1750 RPM with a max 1HP, then you can purchase a single phase AC motor that doesn't require a converter.
If you need to control the motor speed or torque, though, then your motor choice is fine.
A single phase to three phase converter is usually referred to as a motor drive in this case, since you aren't merely converting the single phase to three phase, but driving the motor with specific parameters.
Make sure your motor drive supports 120VAC input, and 230 or 460VAC output. One such driver is a Schneider Electric ATV12H075F1. It should run your motor just fine, but consider talking with a specialist to verify - I've not personally used this drive or the motor you've chosen and have only given each a cursory glance. It may not drive your specific motor, so consult both data sheets or work with an expert.
Again, while you can buy a simple converter that doesn't attempt to drive the motor, there's little reason to do this - just get a single phase motor.
What size wires do I need for the plug from from the house to the on/off switch? From the switch to the converter and from the converter to the motor?
From the driver to the motor:
Your 1HP 3 phase motor will draw 3.3A at 208-230VAC, or 1.7A at 460VAC. While you should consult your driver for the voltage and thus find out the amperage, the reality is that you shouldn't use anything smaller than 14awg wire for this job, and 14 awg wire will handle both currents well, so plan on 14awg wire for this run.
From the power source to the driver:
Your motor drive will have an efficiency rating, indicating that it will use more energy to run the motor than the motor will output. Further your motor won't be 100% efficient either. 1HP is about 750 watts, but due to loss of efficiency you can expect to use a quarter or more of that at the power source. So we'll round up to 1,000watts, or just under 10A at 120VAC from your plug to the driver. Assuming the driver is located close to the motor, and this single phase run is 75 feet, then you could safely use 14 awg, but you'd have a 5 volt drop in this run, and at 10 amps you're losing 50 watts heating the wire. I'd feel more comfortable with 12 awg wire for this run.
I would like to plug this into a regular 15 amp receptacle-the motor will be about 75 feet from the receptacle.
I'd recommend keeping the driver close to the motor, as you'll need to run four or more wires between the driver and motor, vs 3 between the power source and driver. This will reduce your total wiring cost. However, the higher voltage and lower current of the 3 phase means the wiring losses are lower, so the setup is slightly more efficient if the long run is 3 phase. The difference in efficiency is negligible, though, and if you have any other requirements that suggest a specific placement for the driver then they should probably weigh more heavily than initial wiring cost or overall efficiency.