AC Inverter
We decided to go with an induction cooktop, since it's so much faster and cleaner than gas. That meant we needed a powerful AC inverter.
We bought the 3000W Renogy Pure Sine Wave Inverter, it's been working flawlessly!
I bought this gear with my own money, and no one is paying me to write this, but the links here are Amazon Associate affiliate links that help support my content - and they don't cost you anything - same price as if you went to Amazon directly!

Fuse for inverter
The fuse you use between the battery and inverter is VERY IMPORTANT, since it's carrying a HIGH amperage, meaning cheap-quality fuses will melt (I had it happen).
Make sure to buy the type of fuse where you have to have actual crimped connectors, you need a solid metal-on-metal connection.
I bought the Renogy 400A Set w Holder ANL Fuse after a previous cheaper one melted, and the Renogy one has been working flawlessly. It's worth it going name brand!
Stove
For our stove, we got the Nuwave Gold Precision Induction Cooktop, it's way better than the Duxtop brand... the Duxtop doesn't let you "simmer" things at a low enough setting, meaning you'll even burn oatmeal! But the Nuwave works perfectly for oatmeal and other lower-temp simmers, and also heats up crazy fast, and has tons of temperature levels for precise cooking! You can also build a leveling stove top!