Runs down the passenger (LHD) side of the vehicle. I would ensure it is fused appropriately (many inverters specify a Class T fuse) and the entirety of the cable run is correct for what the inverter calls for.
Speaking of what size to go with, that's personal preference and space dependent. Where did you want to mount it?
Also, what are you planning on running from it? And for any extended time? The factory battery (or aux battery) can supply approximately 50Ah before discharging to a state of damage to the cells (50% SoC), so that equates to a 100A load for 30 minutes, or 200A load for 15 minutes. 200A load, with a 87% efficiency is around 2,000w of inverter output; half that to approximately 1,000w for a 100A load for 30 minutes. Since you brought up induction cook top, most of those will draw 1200-1500w, so a 2,000w inverter is probably about right (or something in the 2KVA range, depending on how the brand lists it)
Going huge on the inverter isn't always a great plan because it also is often a little less efficient than appropriately sizing it for the load you plan on putting on it.
My build spreadsheet involves adding a Victron Phoenix 12/1200 inverter, although I need to measure to see where I can fit it; at current my plan is to feed it from a 135Ah LiFePO4 battery; of course, that could change