Multiple Power Sources - How to I combine ?

An inverter/charger usually has an AC transfer switch built in. When it sees an AC input, it passes the AC current through to loads, and uses some to charge batteries. In this mode, it's supplying DC current to the batteries, and passing AC through (but not inverting from DC). The Classic may also be supplying DC to the batteries if there's sun, and depending on the interaction of voltage setting on the charger and the Classic. There's no problem with multiple DC sources charging the batteries, but it's normally most efficient to use generator power just for bulk charging if necessary, and let solar finish in absorb.

When there is no AC input (and only then), the inverter reverses the DC/AC flow, and supplies AC power to loads. If and to the extent the classic has power from pv, it will help supply the DC current to power loads.

I don't know about the Aims inverter in particular, but that's how inverter/chargers generally work.

Some have multiple inputs, and can differentiate between shore power vs generator power, but the Aims likely doesn't. As as far as switching between AC, you are the transfer switch when you plug/unplug the various external AC sources. It likely only knows if it sees an AC input or not, so you'll want to manually manage things like only bulk charging with the generator, but getting to float on shore power.

This also assumes things are properly wired, so you aren't, for example, backfeeding generator or shore power into the inverter AC output ;-)

Maybe an ISMI catcher? Surely they run on DC though, so no inverter needed

My 45a Morningstar PWMs are fanless, but not silent (they make a fairly loud high pitched buzz at times). Probably just the PWM though, and IIRC there may be a setting (which MS recommends not using) to reduce or eliminate it. Mine are in a crawlspace though, so it's not an issue for me.