Thanks for the input and info. I currently have no system at all, I am wondering if I can do some PV without any permitting and that is why I ask these questions. I have a remote shop area that has no power other than a gas power generator.
To answer your questions, I have no invertor yet either. I do understand your point on the three phase, is that something I should consider for a heat pump? If I had a grid tie system I assume that would not be a reasonable option, is that correct.
With grid-tie you wouldn't worry about when it draws how much power, nor about starting surge. So only cost, lifespan, efficiency, noise level would matter. No need to spend extra to match power draw to variable source. Grid-tie PV on a net-metering plan, no batteries, is the most economical and efficient.
Mass-marketed consumer products will be the lowest cost, and 3-phase commercial units would likely be more expensive. Searching a little I haven't spotted a suitable 3-phase heat pump yet, but I did find variable speed. Trane had several models, and the variable speed of course was the most expensive. That would be 3-phase motor and VFD built in.
Split-compact units are often variable speed, and those are low cost. Not sure their lifespan - Trane indicated 15 to 20 years for their large units.
Since you have no power in the shop, you could set up an off-grid PV system to run it. Maybe have battery state of charge feed a control loop that runs the heat-pump temperature setting up & down to just consume surplus energy and not run battery down. Heat (or cool) a tank of water as thermal storage and use that to heat and cool the building. You might need a separate dehumidifier or window A/C to control humidity if that's a problem in the summer.
Batteries - Several choices are maintenance free AGM lead-acid (70% discharge 500 cycles, 15% discharge 5000 cycles), wet-cell golf-cart or forklift (lower cost, more cycles), Lithium (deep discharges 5000 cycles)
Lithium typically has similar cost to lead-acid per kWh of cycle, but costs more up front for more cycles. Some of they guys here are setting up DIY lithium for similar capital cost to commercial AGM batteries but with 10x longer life. I use AGM for lower cost no maintenance, occasional cycle during power failures. If your application doesn't drain batteries after dark, might last 10 years for you.
What I have is a large PV array and undersized battery bank (about 1/4 the size vendor recommends.) The PV is AC coupled (grid tie inverters) and Sunny Island battery inverters charge at appropriate current - when off grid PV production is curtailed to match load. If you have an electric start or manual generator, that can be used to support load and recharge battery.
With a generator, you can do combined heat and power - since you will often have insufficient sun in the winter, capture heat from generator's cooling system and exhaust pipe to heat the water tank, while also using the electricity. If air-cooled, could run the cold water return from system past a radiator in the airflow first to capture some of its heat.