I've begun calling my new character an Arcane Assassin { he's essentially a sneaky mage. }

His arsenal of attacks will include utilizing illusion spells to make a sneaky kill with bound weaponry.

I was leaning towards the Nightingale armor set, but, I'm not really sure anymore. Suggestions?

The Nightingale armor is okay, and looks good.
But it comes enchanted and you need a mod to get it unenchanted...
Also, it doesn't Smith up too high because (like Thieves Guild or basic Leather armor) there is no Smithing perk applied.
(As an example, basic Scaled armor Smiths up extremely high.)

Lately my guy wears the blackest color Vampire armor with Dragonscale light hand and foot, and a long black light armor fur cowl.
Looks killer! Very sinister. Smiths up to ~600 armor rating too (with no shield).
Everything double-enchanted, and I can wear a circlet under the hood too.
Grab the Cowl mod (if you're on PC), which is on the Workshop:
"Fur Hoods HD" by Northborn. I couldn't imagine playing without it...

EDIT: I use The Lord Stone (standing stone) and Locket of Saint Jiub to reach 500+ armor rating (depending on skill) without a shield.
And then Ebonyflesh can of course add an additional 100 rating on top of that...

If we are talking armor, it would be dragonscale. If we are talking about what we prefer look wise, I'd go Glass Armor with a mage hood. It blends in pretty well and looks like a spellsword set. Otherwise, in all honesty, I really like the guard/stormcloak armors. Lots of colors to choose from at least lol.

Learn smithing and enchanting and then use whatever armor you like, with whatever enchatnments you want.

Stalhrim light with a mage hood, all nice and evenly enchanted of course.

I quite like the appearance of Elven armor. It works well with a lot of different kinds of characters, in my opinion.

Scaled Armor

Mage Hood

Leather Bracers

Vampire/Leather Boots

DR is pretty good and you'll look like a standard adventurer/merc/bodyguard, which is good for an assassin.

Depends on your personal taste. All of my favorite armors are from mods and even then I like to mix and match pieces instead of wearing a matching set.

My Imperial Battlemage wears full Dragonscale with the Mages Hood you can buy at the Mages Guild. (unenchanted version so I can put my personal enchantments on)