Never had a moment's problem with mine. High mileage is not an issue. They have been, for many years, the bike of choice for round the world riders - as you'll see from many of the threads here.
You shouldn't have too much trouble finding a good one in the price range you have stipulated.
They are also extremely economical.
I averaged 90mpg on mine,
loaded or not and no matter what my riding style.
However, if you've not ridden one before they do take a bit of getting used to. They are distinctly "agricultural" in sound and gear changes can be a bit clunky. But they're fantastic bikes. I also found the lower centre of gravity brilliant for low speed maneuvering.
Bloody hell

I need to learn your riding style



Maybe a typo?
I'd say more like 60-80mpg if ridden steadily.
We've had three 650GS's one a Dakar. A 2000, 01 and an 04, all very nice bikes.
The 04 was bought as 'just in-case bike' when the 01 had developed a running problem which we were unable to identity, and were due to leave for a trip to the alps a week or so later. The problem turned out to be the Lamda sensor.
My other half ended up taking the 04 on the trip. This bike had 38'000+ mls on it and had been used in Bolivia and then as a daily commuter by it's original owner. It ran perfectly for the whole trip returning upwards of 70mpg fully loaded with gear for two weeks in the saddle, covering 2700 miles.
After returning home SWMBO decided to sell it on because she 1, didn't need two and 2, because it had renthal bars fitted which were too wide and forward for her comfort.
The new owner uses it for his daily commute carrying his wife on the back and tells me he's now covered over 6000 mls on it, and loves it
I wouldn't hesitate to consider a well looked after (proven home maintenance is fine) 650 with anything upto about 80'000 mls before I started to worry.
Your right on the money with your budget. You should be able find quite a nice bike with some service history on it, possibly even upto a 2005 model.
If you're considering doing your own servicing, it's worth noting that the older single spark bikes will cost a little less by virtue of only having one spark plug.
They're also better if your planning to off road the bike, as it's easier (Though not that easy) to get at the spark plug should you drown it in a river
Good luck, and don't forget to post a picture of your new steed for us all to see.
Val.