There are two types of problems you'll need to overcome:
- High instantaneous loads, such as compressors and some well pumps, require high-output batteries and inverter. Though you state startup requires 800 W, for a second or so, it might draw several times as much power. A 3 kW inverter probably can handle that, using a few batteries in parallel. This should work, since well pumps run intermittently and likely won't deplete the battery in the long run.
- Refrigeration loads run frequently, and are often the biggest energy consumer in a household. You'd need a large photovoltaic array to charge in daylight, and large capacity batteries to run the fridge at night and when the sun is not at optimum angle. You might be better off using a small automotive refrigerator or marine refrigerator, designed to run directly from batteries sans inverter. They have less room, and likely cannot keep ice cream solid, but are generally more practical off-the-grid.
A home rerigerator might use ~30-150 kW-Hours/mo, ~1-5 kW-hours/day, and you'd need about three times that capacity in solar generation, because panels are rated for peak output, in direct, perpendicular, sunlight. You'll also need additional storage capacity for rainy periods. For a 0.4 cubic meter (14 cubic foot) high-efficiency home refrigerator, that comes to ~3,000 watts in photovoltaic panels, and ~3,000 watt/hours (250 ampere-hours at 12 volts) in batteries to run just the fridge daily and for two rainy days. You can perform the same calculations for a specific high-efficiency automotive or marine refrigerator. If you have access to cold ocean water, some marine fridges can use that to cool the condenser unit, making the device more efficient.
Hint: If the power fails, eat the ice cream first. ;-)
However, if you're already wired into a local energy supplier, can you sell back any excess electricity generated? That obviates the need for expensive storage batteries with limited life-span. In the USA, for example, "With a grid-connected system, when your renewable energy system generates more electricity than you can use at that moment, the electricity goes onto the electric grid for your utility to use elsewhere. The Public Utility Regulatory Policy Act... requires power providers to purchase excess power..." Look into option this in the Caribbean, where you live,