VERY SIMPLE.
If your new inverter has a built in transfer switch (often called "pass through feature"), wire like this:
Shore power in to main breaker box.
Separate fuse in main breaker box for inverter IN
Inverter OUT to sub-panel of only those things you want powered by inverter.
If the new inverter does not have a built in transfer switch, you will need to add one. Wiring would be:
Shore power in to main breaker box.
Separate fuse in main breaker box to new ATS
Inverter OUT new ATS
New ATS to sub-panel of only those things you want powered by inverter.