I tend to buy DH's at T M Lewin, they seem to have a permanent sale on. He prefers a double cuff (ones you fold over and need cufflinks for) but it depends on the person. I once bought someone really nice cufflinks for their 40th and their still unworn now it's their 50th! Fabric silk knot cufflinks could be a good purchase and you could replace with something nicer if they get worn.
TM Lewin, definitely. They measure you up and give you a shirt that's the right sleeve length, collar size and fitted (normal), semi-fitted (fat bloke) or unfitted (who ate all the pies?). THEN you get to decide on collar shape, style, colour, pattern. Cuff-links and pocket handkerchieves look fine for execs, accountants, lawyers - double-cuffs and hankies on a bog-standard office worker just look like he's trying too hard (and they catch on the keyboard...
Charles Tyrwhitt are fine, but IMHO they're not as good as Lewin's.
I am not a Dad, but DH like Thomas Pink and Charles Trywitt. Also Van Heuson (SP sorry) and Jaegar. If you are near the Swindon outlet centre (or even an hours drive away from any Glen McArthur outlet) it is worth going for the shirts and discounts on them there.
Tyrwhitt are easier to iron than Lewin! That counts in this household
DH gets his in the 4 for £100 offer in Tyrwhitt, which never seems to end. He goes for double cuff with links and normal collars as cutaway collars are awful beyond belief. They also measure you up and do different sleeve lengths like Lewin. The 100% cotton non-iron ones are the best!