What you are talking about is typically represented as a "hybrid inverter". There are two broad classes, component inverters, and AllinOne inverters.
The component hybrid systems are assembled from individual components, an inverter, a charge controller, battery bank, and solar input. The highest quality, tier-1 products are typically, but not always components.
The AllinOne systems, or AiO, is an inverter, charge controller, battery charger, all built into one box. Buy the box and you have everything included. AiOs though tend to occupy the lower end of the quality spectrum, but not always.
Typically a hybrid inverter will be powered via a DC battery bank, either 12, 24, or 48V. The inverter then makes 120VAC (or 120/240VAC) that the house uses. ACout terminals somewhere on the inverter lead out to your main electrical panel, to power your loads.
A hybrid will also have ACin terminals to accept power from the grid or a generator. My XW+ has two ACins, one for the grid, and a second for a generator. It has an automatic transfer switch built-in. That is so grid(generator) power and the inverter power can never meet. You hook up a standard inverter to your electrical panel the same way, but you MUST install your own transfer switch.
Before you make a decision on what to buy, you need to slow down a bit and draft up an itemized list of what it is you want to power. A good rule of thumb is to have at least 2X the inverter capacity of your single largest load. To me, 3000W is a bit small for a 48V inverter, so you really need to pin down your power consumption first.