Would you say by joining Thieves Guild before anything else, as a character that uses

• Destruction spells
  
• Illusion spells
  
• Alteration spells

And only wear cloth.. Would a character, such.. fit within the Thieves Guild? If the person would only steal what is needed, never more, never greedy. Steal for the poor?
Would it say, ah! Such Mage-like character join this guild be having no moral, RP sense would not fit to join later on the Colleage of Winterhooflidoof?

And is there room for clothie Thieves Guild? *no spoilers*

Compared to oblivion, the SK TG is a lot more "evil". In oblivion i almost felt as Robin hood, but you are more a thug in Skyrim, so keep that in mind if your char is good. The quest line also includes some great stealth opportunity's, so go with sneak.

Invisibility will work for that yeah?

Of course. I also recall some situations where i had to pick difficult locks. To answer your firs question; no, you are not required wear anything special.