Except for the six years when I lived on a couple of acres, I've been using a reel mower (manual push mower) since 1987 (and before that, I used one as a kid). I find no problems with the cut, especially since they've improved the mowers over the past 10 years or so. You won't be able to cut it to the 7.5cm minimum recommended, but I usually cut mine to 5-6cm or so.
Reel mowers cleanly cut the blades, while rotary mowers often shred them, which is why most golf courses in the northern US use large banks of reel mowers for their fairways (not sure what they use in warm-season areas). A good reel mower is not inexpensive, but there is little maintenance other than annual or semi-annual sharpening, which isn't much of a problem, and you get a nice workout while mowing. And given the size of your lawn, you probably can get by with a less-expensive model - just make sure you get one that's easily height-adjustable.
One important point to note is the type of grass you'll be cutting - the finer the blade, the more difficult it will be to cut to 5cm + length (the finer grasses can flop at that height). If you have bluegrass or a healthy mix of bluegrass,ryegrass and fescue, you should be fine.
There is at least one poster here who'll give you a completely different opinion - whom you believe is up to you :) To bolster my case : http://caltrimmer.com/products/features/reel-vs-rotary-comparison/ and https://www.toolboxgeeks.com/reel-mowers-vs-rotary-mowers/ (notes that rotary mowers have mulching possibilities - an excellent point), and here - another old guy's opinion (but he's from the UK, not the US): https://betterhomesteading.com/homestead-garden/lawn-care/manual-push-reel-mower-vs-electric-rotary-mower/