1 or 2x – and any reason why 10 spd?

The answer is probably in the question. Deore! It’s cheap, robust and unlike Deore of old doesn’t weigh as much as the moon. The cassette which is still 11/42 weighs less then the 11sp SLX or XT cassette.

There isn’t always an advantage in buying as a job lot from one place you could probably pick up Deore 11-42 cassette and shifter for not much by shopping around, including the german sites which don’t automatically crop up on Google (although there is shipping to account for).

Mech – unless you want all from the same group, whichever of the m6000/7000/8000 10 or 11 speed mechs should work fine. I’ve just picked up an SLX 11-speed mech for my 10-speed setup for 40ish in the CRC sale. Cassette was 25 quid or so from Bike-Discount.de – they also have a deore RH shifter for under a tenner.

Depends how fussy you are.