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AC as much as you can. Wiring thickness quickly becomes a limiting factor so you site your inverters right next to your battery banks and you keep your solar voltage as high as your inverter allows you to (up to 400V these days).

Modern systems with multiple DC sources are usually all tied to a common DC bus (24-60V depending) that is parallel with the batteries. Devices called charge controllers take the unregulated DC from a DC source (PV, Wind, hydro...) and output a constant voltage which can be used to charge the batteries or be directly consumed by the inverters. The inverter takes care of tying the DC bus to the AC side of things including the grid and/or generator. Modern DC tied inverters perform multiple functions as they can be programmed to use AC or DC as the source, charge the batteries and even feed power back into the grid.

You can do it either way.

Tying together with DC usually works out cheaper, since MPPT tracking buck converters to charge the batteries are cheaper than having extra inverter capacity.

As a bonus, you can buy quite a lot of 12V DC equipment made for cars and caravans which tends to be a lot more energy efficient.