With 400 square meters, it's worth switching to a motorized lawnmower, otherwise you'll wreck your back for nothing. Among the three options, the battery-powered one is what I'd recommend if your lawn is all in one area with no weird obstacles. Modern battery-powered mowers have more than enough runtime for 400 square meters, they charge quickly, zero maintenance, and the noise is basically nonexistent. The downside is the initial cost, but if you already own other tools with the same battery (like a string trimmer or leaf blower) at least you're spreading out the investment.
Gas is a pain: you have to start it every time, it pollutes, it stinks, it's crazy loud. It's fine if you have a farm, not for a regular lawn. The corded one is even worse because you can't go everywhere, the cord tangles up, you risk cutting right through it, and anyway it drains your energy because you're dragging it around. The only situation where a corded mower makes sense is if your lawn is small or if you use it like once a year.
I see people in my clinic who made this choice, and most of the battery-powered owners are happy, especially in summer when you're mowing frequently. If you want to save a bit upfront, at least get one with a battery even if it's not a fancy brand, rather than spend more on a gas one. Among the main brands, Husqvarna, Makita, Worx, DeWalt are all fine. You don't need some professional-grade thing for a residential lawn.