Well first off you need nightingale armor.....maybe get the pugilist gloves for fisticuffs?
sneak up on people and snap their necks lol
One Handed and illusion/alteration. Fear and Frenzy seem perfect for a league of shadows build. there should be a one-handed katana in the secret room in riverwood once you're good with delphine. paralyze and fear should be excellent choices for bringing it down to single combat. maybe even go as far as using alchemy and pickpocket, planting poisons on people. Invisibility and maybe have the darkbrotherhood gauntlets on backup for the backstab bonus. sounds like it would be a fun build.
i might go ebony mail and just the hood of the nightinggale armor, i think only batman has the cape. Daedric Gauntlets would be a good aesthetic choice i think, they are the only ones i can think of that have the 'spikes' on the forearms.
Batman is going to pick pockets? Or is that to plant poisons?
plant poisons, i would only use archery as a utility skill, without putting any actually points into it, what comes to mind with this build is crossbows+explosive bolts. simulate the bombs they would use. or fireballs.
invisibility pots from alchemy, save on points put into magicka. also slow poisons for for dragons. for followers..... none come to mind except for cicero. but i've never had him as a follower so i dont know how he is.
well, without illusion it might be interesting. my 'talia' character has been doing great, she got her katana without having to start the main quest, RPing it as she killed the man who betrayed her to the legion and stole her blade (fultheim). the illusion spells look like you could roleplay them as throwing gas bombs or pellets at the enemy. so theres that little stretch.
alchemy will definitely be relied upon heavily. there is this utility i always use when starting up a nice batch of potions http://skyrim.warlore.org/ just the skyrim alchemy tool. slow poisons will be necessary without the crowd control illusion can give. deathbell and salt piles give you slow. throw in any damage health ingredient to give you a decent poison. i suggest completing the 'Crimson Nirnroot" quest. "Return to Your Roots" i think it is called. gives you a great passive for alchemy. 25% chance for a duplicate potion.
Pickpocket i've never gotten the hang of, basically the more valuable it is, the less likely you are to place/take it.
I've never actually used cicero as a follower so i dont really know much about him, just that a fair number of people love him.
Hmm. Well I'd say, get a Blades Sword ASAP. Ebony Blade could work too though, but it'll hinder your use of spells, should you choose to use any.
Definitely use Illusion if you plan on using magic. I'd stick with mainly Frenzy, but throw in some fear too. An assassin from the League is very skilled in the art of deception.
For armor, I'd say Dark Brotherhood cowl (LOA assassins are often depicted with the face cloth over their mouths), Ebony Mail, Nightingale Gloves, and Ebony Boots. Full Nightingale + DB cowl could work too.
For RP, I'd say play as an Imperial. That's what I'd imagine Talia or Ra's to be.
Destroy the Dark Brotherhood whenever you get the chance. The League of Assassins would see them as a blight on Nirn honestly, and they would need to be purged. The LOA is more about order and rebirth, the DB is more about senseless chaos and destruction.
I'll write more tomorrow since it's 2 AM and I'm very tired, and this RP really intrigues me (I'm a massive Batman fan, in case you couldn't tell). Maybe I'll try to think of a way to work in the Lazarus Pit...