I also don't like inverters for powering a PC.
They are not the best choice for a PC install for a lot of reasons. They're not good for a laptop for even more reasons.
If you're dead-set on using an inverter, you should wire it straight to the battery.
If the inverter has a remote lead, then wire that you can put a switch on that line and wire it to your 12v source (battery) and use the switch to power the inverter on/off.
If the inverter does
not have a remote lead, you can use a relay with a switch to power the inverter on/off with the switch.
Honestly, I'd look into a DC-DC power supply.
An inverter converts DC from the car to AC for a home electrical outlet. The laptop's PSU will convert AC back to DC which the PC uses. It's an inefficient process that can create noise in your audio system and generates heat. It also introduces more connections and more potential points of failure in your setup.
A DC-DC power supply is far more efficient than an inverter for this purpose as it doesn't do the double-conversion.