you're one cheap n dirty rver to not want to bother with a solenoid which is also cheap. I think solenoid would be easier than an anderson plug.
a ring terminal on the positive off of the battery then you can ground the negative cable on the frame anywhere.
You can find 12+ going into your fuse box under the hood also, but I would be weary of pulling so many amps through the wires that provide power to run the vehicle too.
Adding a lot of connections at the battery is not good for the reason that there can be so much corrosion at the battery due to gasses from the battery. Many modern vehicles will have one connection that goes a few inches away and then everything gets attached there just to avoid some possible corrosion issues down the road.
You can also get your 12+ off of the starter motor under the vehicle. There is a very heavy gauge wire leading to that and it is only used for starting the motor, never during the drive, so is available to power your inverter during the drive. This gets closer, possibly, to where your inverter will be and gets you away from another battery connection at the battery. Electrically there is no difference, but requires more care running wires under the vehicle.
Be careful, the starter power feed wire is hot all the time.
Disconnect battery to do work if you want to be safest. Stray electrical surges, from the sparks you might get touching 12+ to ground, could damage electronics - though rare, "could".
As far as plugging and unplugging an Anderson plug, no issues there, again, electrically it is the same as an "on" solenoid. Turn the inverter on after you plug in, off before you unplug.