I have been struggling for the last month to create a new character in Skyrim. I developed a little background story. Do you think it is viable?

That is a very good background.

Though, Nightingale Armor doesn't seem like something an assassin would use.

Thanks, what armor do you suggest for an assassin?

I think it fits an assassin very well

A true assassin should be as inconspicuous as possible so they should wear normal clothes to blend in or maybe guards armor for the hold that they're in. I feel that the Dark Brotherhood gimp suit is just plain ridiculous as you might as well wear a sign that says "Hi I'm in the Brotherhood and come to kill you".

Haggar, I did not specify that in the topic but when I roleplay as an assassin, I do have clothes with me all the time. When I am entering a city I always dress them.
Sometimes I wear my assassin armor inside the city (and if that's the case, I only use the Nightingale Armor because it covers my face), but I make sure to change all my clothes when I am entering my house or when I am going to talk to an NPC without anyone watching me, of course.

Although I always create morally good characters, I keep the secret identity of my assassin as an high priority.
If a guard recognizes me as being a Dark Brotherhood member or a Nightingale, I kill him (without anyone noticing). Plain and simple.
I don't mind being recognized as a Thieves Guild member. The Lore says the Imperials accept them because:

So, I don't really mind about that.

Only the Skyrim Guild maintains any relations with the Brotherhood. Morrowind's and Cyrodiil's guilds don't.

@LordoBones Thank you, I did not know that. I guess that makes the story a little more plausible.

Wow I never though of that when RPing an assassin. Now I wanna make one...lol

The Nightingale Armour is a cool look for an Assassin.

Much more appropriate than the DB "jumpsuit"

ha well I borrowed a bit from my favorite assassin...Agent 47

Daniel I like the way you RP, being careful not to show your face in situations and not being seen at home