even if they (at least the yaris and prius from the 00s) drive pretty badly
For a first car at your budget, this should be the least of your concerns. A Yaris or Aygo (or even the Aygo's Peugeot/Citroen siblings) are perfect first cars. You are not going to get any performance-type vehicle with what you can afford right now, so this should be the last thing you prioritize. If you really want some semblance of performance, find a Peugeot 206 or something.
But the aygos sold here for that price have extremely high mileage (as in 160k+)
How old are you? Any modern-ish car made in the last 20-30 YEARS should be able to achieve 200k miles at the minimum with proper maintenance. Just make sure the MOT is up to date, not falsified by a shitty shop, and you should be fine.
Case in point: my wife's 2015 Toyota Highlander with 128k miles (206k km) and still drives like new.
Another example: my 2008 Toyota Sienna with 278k miles (447k km). While it's not the prettiest with patchwork paint from sun damage and parking lots, mechanically it's damn near perfect with not a speck of rust.
And finally.... laughs in a very rusty 487k miles (784k km)