Modified sine wave inverters cause electric motors to run hot.
Pure sine wave inverters are 3 to 10x more expensive for the same wattage.
The Solar charge controller should be programmable. If the battery is being cycled daily, the voltage setpoints are different than if it were not used overnight, 2+ hours at 14.2+ volts when the battery is not discharged the night before will lead to positive plate shedding and extensive water use.(premature battery death)
True 12v deep cycle batteries are rare and 30% more expensive than marine batteries easily obtainable. Marine/RV batteries are hybrid/ dual purpose batteries much closer to starting batteries than real deep cycle, and a starter battery deeply cycled will not last.
So by the time you get and wire up a battery, inverter, solar panel and charge controller you are looking at a considerable investment that could be bypassed by having battery powered angle grinder and a headlamp you take with you from the main house.
Now if you were wanting to keep a 12v compressor fridge in the shed with some frosties, and to power the lights and grinder, then I can help with recommendations, but setting up this system just for the occasional late night lawn mower blade sharpening seems wasteful.
If you are wanting to run a cheaper 120v dorm fridge on an inverter, double the battery capacity and solar panel and get an inverter with a standby feature.