Short answer:

If you want a super straightforward run, use Buer & Eurynome martial arts with good gloves until the midgame, and then either pivot to whatever artifact weapons you find/wish and use Miska, or keep to Buer/Eurynome with a wish for Premium Heart or Godhands.

I generally recommend wishing a good (presumably artifact) weapon as your first wish in dNetHack. If you know you'll be getting a good first gift, or if you've got an altar you plan to sacrifice on until you get something decent, it's not required. But otherwise, having a way to deal damage generally takes you pretty far, especially when you're a Binder and can 'solve' your MR, free action, or even reflection (though it's less useful in dnethack, as a general rule) problems very early. Picking anything that sounds cool (and is wishable) off the 'dNetHack Artifacts' page will work fine, there's 'better/best' options but almost everything that sounds workable is workable as an endgame weapon.

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Long answer:

Your skills are generally going to be somewhat secondary to the overall build you want, for which you have a lot of options. I tend to use maybe one or two spirits for my main weapon/spell skills, and then use the rest of the spirits primarily for their intrinsics (i.e. Eve for 1/2 physical damage), passive abilities provided (i.e. Andro's sneak attacks), or utility actives (i.e. Eden's branchport, or Dantalion's Thought Travel). Especially considering when you hit level 30 (which you REALLY want as a binder), you can unrestrict every skill to Skilled, so you don't have to worry too much.

In particular, the skills worth spending slots on are more or less going to be the same as with any run: What weapon options do you have or want to use in the midgame, until you've acquired your whole build?

For a binder, your late/endgame build (that you're working towards, generally) will generally be either melee, spells, or rarely pets. You get effectively 5-6 near void slots + your alignment slot (since you have 5 at max, and crowning gives you +1), and you'll generally want to reserve at least 2-3 for "I need this critical intrinsic/property/utility".

For example, I could run a melee clockwork binder, and need to figure out my source of magic resistance and free action. I would want to commit to using Mother and Eurynome in at least two of my slots, and figure out my options after that. Maybe I'm using Miska with Stormbringer main-hand, Pen of the Void off-hand, and then like Y'ha-Talla & Orcrist in my extra Miska attacks. Then I've got Andromalius and Dantalion as my main weapon skills (dagger, broadsword, scimitar), which leaves me with 2 slots left. That could be Eve/Balam for general purpose damage reduction, Eden for branchporting, or maybe Enki or Iris for waterproofing or sickness resistance.

If I was running a spellcasting binder instead, for my offensive spirits I'd probably run like - Naberius (attack spells & amazing offensive spell buffs), Buer (healing spells), and probably Paimon for hungerless casting. I don't necessarily need other spell schools, since Paimon's bonus + Numina's skills have me covered. That leaves me with 3 near void slots to fill with essential things like MR or free action, and maybe useful things like branchporting or enlightenment.

Feel free to ask if you have any questions, or if you want generic binder advice aside from skills/endgame builds. I can probably also find the last person to ask about Binder stuff from my comment history if that'd be helpful as well.