That's a Gainward card; those were very well regarded in their day for overclockability and performance. For 30 EUR it's perhaps a little high all things considered, but it looks mostly complete, and it sounds like you want the specific model so I'd say it isn't too bad. 200 EUR is hilarious for a 6800 Ultra though.
I can speak from experience about the WinFast A400 - the cooler is nothing special at all (I have A400GT, which is the same cooler/board ref as A400 Ultra, it just lacks one of the power connectors and has slower memory); it doesn't run all that much cooler, and the fan is not reliable. Zalman VF-700 performs better, is quieter, and makes for a much lighter card.
As far as games - I remember Doom 3 being very playable with high-ish settings on the 6800GT, and I remember Carmack talking about how Doom 3's "Ultra" setting required a 512MB card. The 6800GT couldn't quite do "Ultra", but a few years later my 256MB 7900 had no problems with it. 🤣 Games from 2005 and later will be kind of a mixed bag with GeForce 6 (especially with the AthlonXP and its lack of SSE2/3) - it technically meets the system requirements of *a lot* of games up through at least 2010, but certain features (like HDR) will incur massive performance penalties compared to later cards. For UT2003 or Doom 3 though, it should be perfect.
swaaye: I thought the "Ultra Extreme" was only available as a 256MB AGP board (and is/was very rare), while the 512MB variant was commonly a PCI-E part (and iirc most of those ended up in Macs).