In past versions of the elder scrolls and many other RPGs, thieves play with light armor. Is this also the case for skyrim?

As far as I understand, both heavy and light armor affects sneaking, but as you are playing close combat, you will want to have at least some armor. 

What type of armor is common for a thief, and why? 

Is using spells for armor(stoneflesh etc) a good idea, or do they cause detection?