Yes, helmet of brilliance is useful. But I would rather wait with wishing for it until you have other parts of the set (SoCM, a good wand of cloning/mirroring, scrolls of charging) and only HoB is missing. Of course if you have HoB and miss e.g. SoCM then go for SoCM. (Note that you can actually wish for "socm", the game recognizes this abbreviation.)
I don't think mirroring has a higher number of charges on average, I suppose they both have a random number of charges between 1 and 3 (that's what it is written in script, but it still might be modified by the program). However, mirroring allows 6 mirrored scrolls per charge if used well.
I am not sure how breaking wands of mirroring/cloning works, but my calculations suggest that by wishing for a wand you get 3 charges on average (including breaking), while by wishing for a SoC you get as many charges as your most powerful wand has. So usually you should wish for wands until you have a powerful one, and then a scroll of charging (although the difference is small).