Normal coins (like modern coins that I don't seriously collect, or the tons of Yugoslavia, Spanish pre-Euro, etc. coins that I get in bulk lots) are kept in zip-lock bags which are grouped together by country/continent in a file binder and kept on a bookshelf.
Coins that I actively collect (My British monarch collection (so far at Charles II), my Swiss collection, US collection, Commonwealth collection, etc.) or coins that just seem pretty are kept in coin albums or in 2x2s.
Proof sets and Bullion are kept in a big chest thats tucked away in a safe corner, generally when showing people some coins from my collection I never show them whats in the chest, only the stuff in my coin albums or file binders.
Banknotes are stored in a delft tin box that looks almost like this one
Even though I like collecting banknotes, I don't have one thats valuable enough that can't be placed in the tin box.
And for safety, my collection is guarded by my three tiny yet ferocious dogs (Well...one is insane, the other two just have a strong bark).
But since I'm away for university currently, everything I buy goes in to a coin album or in 2x2s which are kept in a tin box.