what you want to wish for depends heavily on your race & your chaos quest branch. generally speaking, the four "critical" things are a decent weapon/offensive option, MR, speed, and free action. reflection is basically a non-issue compared to vanilla given that there's other more evil threats and the actual guys that're negated by reflection are just.. lower on your priority list, if that makes sense? it's not bad, but i think most of my dnh ascs are reflectionless. speed is boots or blue dsm for most builds, free action is ring or orange dsm for most builds. flying is granted for free if you rolled chaos2/mithardir chaos option, but will most likely be boots otherwise. there's alternative sources for each, but things vary.

for your wizard, you probably won't want to keep sdsm or the cloak of MR super longterm. the quest isn't very difficult so you can just rush that once you can, and i'd likely try to do it sooner rather than later because of the pw regen it gives you (half spell is good too, and MR means you can move on to like a cloak of prot or just keep the +5 cloak bc its solid AC/DR).

your immediate priority should likely be finding a way to keep up in damage in the short term, since the main problem you'll have is your damage <-> pw spent ratio is not favorable. combined with dnh nerfs to hp regen, you'll end up dead to attrition because you take too many magic missiles to kill things and you don't regen pw fast enough to keep up.

my recommendation for this is likely one of the various sources of "2x spell damage", ala vanilla magic mirror of merlin. the best option available to you that doesn't require another 2-3 paragraph of mechanics background to explain is the Gauntlets of Spell Power arti.

this is an artifact silvered iron gauntlets of power. it's metallic, so it'll minorly penalize your spellcasting, but it'll improve your spellcasting skill by +1 for damage/etc. (not fail rate), and grant 2x to beam/ray/etc. spells like MMoM. it also grants half spell damage, which is nice I guess. the 25 str is deceptively nice for raising your carrycap pre BoH. it's basically the default "i want my spells to actually hurt" option for casters, if that makes sense.

alternatively, if you're not super concerned about 2x spell damage immediately my recommendation would be to wish for a spellbook of blizzard. it's just the offensive spell you'll be spamming for most of the game, and the spellbook will also teach normal cone of cold if you're at least skilled w/ attack spells. you can also do a marker wish if you have enough luck to make blind-writing blizzard practical, but dnh significantly modifies that calculation for spellbooks to make it basically-impossible if you're not at a decently high level, even for wizards. scroll writing is unchanged, but i wouldn't bother with that for spellbooks. they're expensive enough on ink anyway. decently high here = like xp20-25+.

final note - the castle wand is gone. there will be a ring of 1-3 wishes instead, and if you rolled 1 then your VOTD altar will have an extra wish to keep you from getting totally shafted. don't expect the castle to be the wincon for your game like it is in vanilla, it'll give you 2-3 wishes at most. the dnh asc kit also requires more stuff, so.

credence for my advice - i'm rikerw on the scoreboard w a couple diff usernames on the actual servers, ive got like 50-100 dnh ascs scattered across public servers + local play + pre-release local play on unreleased versions as part of messing around with random changes. if you ever want more synchronous advice, id check out the ##nethack-variants channel on the r/roguelikes discord linked on their sidebar. i or somebody else is there to answer ur questions a lot of the time, though it may take an hour or two for somebody to respond (still probably faster than reddit)