"I like your newspaper."
Translation:Deine Zeitung mag ich.
That's correct, too. Syntax can either be subject, verb, object or object, verb, subject. Depending on the context, one might be prefered over the other. Without context, they should both be fine.
Du and Deine are mostly used in lower-case. Using them with capital letters when not the first words of a new sentence is pretty out-dated, but was and sometimes still is used for a more polite or formal 'you' while still being more casual and personal than the actual Sie formal you.