This is a perennial question, so you will find information from past discussions. From memory, the favoured rear tyre for 'mainly road use' (80-20 road) was the Avon Distanzia, although you'll find other recommendations for - and even warnings against - purely-road or 50-50 type tyres.

Use the HUBB searcher with something like "xt600 distanzia t63" (without the quotes) as the searchterm keywords and make different searches as other types of tyre are mentioned/recommended, in order to 'spiral outwards' in your research.

I can sort-of recommend Distanzia on the back, and Pirelli Scorpion MT90 front, "sort of" because that's all I've used on the XT600E so far and it seems pretty good on road, grip-wise, whilst not wearing too fast - although I would say the Distanzia rear is too soft&grippy to last long if you're going to do a lot of motorway / A-road miles. (You could also say that about the XT600, itself!).

I have used a pair of Bridgestone Trail Wing on a Funduro, and they were hard-wearing but scary in the wet. This is a matter of interpretation, though: I have heard both "awful in the wet" and "communicative in the wet" levelled at these tyres and indicating pretty much the same trait - breaking (some) traction early in the wet. It's a bit like that criticism of 4-wheel-drive compared to rear-wheel-drive for cars: rear-wheel slip on rear-wheel drive happens early and is more correctable, but when you really lose all traction in a 4WD car it's likely a bit of a disaster. Ultimately, I prefer the Distanzia to the Trail Wing - but then they were on different bikes, with different characteristics.