Welcome to the boards general.
To your questions:
Yes, you can store stuff in crates and chests, and no, it won't dissapear.
You have to check your stats, when your char is a thief, his preference is usually light armour, but along the road you'll be able to train ALL skills, including medium and heavy armour, so eventually you WILL have benefits from the higher stats of heavy gear. For now, i should try to get my hands on a glass outfit if i were you.
Equipping a shield will not effect your sneak abilities in a negative way.