I think a Yamaha XT600E will probably suffice your needs and tick all those boxes.
It's a legendary RTW bike capable of most things.
The engine is bulletproof which is a plus point.
Most importantly this is a bike which will not break the bank - It's still possible to find low mileage (under 12,000 miles) bikes in the UK for less than £1,500. This represents truly outstanding value compared to a BWM or KTM which you mention a few times.
A BMW/KTM will set you back 4 times what a XT will be but you don't get 4 x more performance.
A KTM is a highly strung machine compared to a XT600E. Yes they are great bikes but are they worth the extra dosh? I say NO!
I did look at getting a brand new Yamaha XT660 Tenere last year but when I had a close look at it I couldn't justify spending £6,000 on a bike almost the same as my mint low mileage XT600E.
BANG FOR BUCK - YOU WON'T BEAT AN XT600E or similar simple robust older machine (in good nick) - XR650, XL600, KLR650 etc...
Then again if you have the money to waste, go right ahead.......
Whatever you deicide, I wish you well.
Ride carefully and Stay safe.
Triumph Bonneville 800 (2004), Yamaha XT600E (1999), Honda XBR500 (1986).