laptop good for HD (1080p)?

So i'm thinking of getting a laptop for school, and while basically a net-laptop will do its job, i want to watch some videos on the laptop. So this raises the question: What kind of things do i have to look for if I want to watch videos on my laptop in HD (like mostly 1080p resoltuion). My budget is under 850$ CAD, and i been told not to go AMD processors, and intel pentium processes for laptops. This leaves me with core 2 duo processors.

So, does the videocard play a major role in the playback video? and how will I know that it is sufficient that it can play 1080p without lag or problems. Or is it entirely CPU based and thus going for better CPU or what? Will integrated be sufficient or do I need a dedicated GPU?