Welcome Graham
It is hard to find a bike that "does it all" better than the K1300S. It's fast (very fast!!!) yet completely usable, comfortable, economical (for a 1300), well mannered and has pretty decent handling. I've always described it as a bike yo can happily ride to the Alps with pillion and luggage in a day then enjoy the passes with the sports bikes the next.
When buying, the newer the better. Get one with a full BMW service history and buy the extended warranty. Check out the various posts on hear about the radiator and check it's not getting close to replacement. While some may disagree, I'd recommend getting one with ESA. The shocks are pretty decent but the ability to switch from comfort to normal to sport while on the move, as the road conditions/mood dictates, is something to cherish.
I hope you have fun shopping, even if the current situation makes it a tad difficult, and look forward to seeing pictures of the bike you eventually buy.