Several of my mates have Shimano brakes and all like them. Either is a good decision. I like Hope for their Britishness too and they are beautifully designed IMO.
As for doubles, the last geared build I did was a double, but I have been doing a bit of SS recently and you soon realise 9 or 10 gears is plenty for around here. (I switched my SS to 1×9 for a bit but found it boring so switched it back).
Anyway for Surrey Hills, I reckon 1xX is plenty. The steep climbs are not long and the long climbs are not steep.