I don't know that I would go for a cheap corded mower. Why, because the cords are a pain in the neck. you have to pretty much keep the cord over your shoulder so you don't run over it. If you have anything that a cord could wrap around, it is going to, I don't care if it is just one small tree in the middle of the yard, it is going to get tangled there. And then if there are flowers that you, your girlfriend or the landlord planted, forget about them still being around after a couple of mowings.
And then there is always the part of running over the cord, of your extension cord being just a little bit to short, and then pulling the plug out. Then the surge to get through that tough clump of grass drawing more power than the circuit breaker can handle and blowing the fuse, or your girlfriend starting the washing machine or dryer that happens to pull on that same circuit breaker. I think if you plan on having a lawn in your future home also, you should go with the middle option and get a mid range quality battery one. You already have some tools from Ryobi check to see if the tool batteries are compatible and go with one of them.
Hm. The lawn is small and the furthest edge isn't more than 20 feet from the house. I really think corded would be fine, but you make some compelling points.
Are you on a long term or short term rental lease, after staying in a "home" versus an apartment complex what are you likely to move into next? Twenty feet for the lawn at this place not bad, but as you need to also,like you do with most of your things, think where am I going to be tomorrow, Three bedrooms, two baths in a modest suburb, or a growing family in the country. You can always rent one for the first couple of mows and see which works best for you, now and might continue to work okay for you in the future.