Need some help creating an effect for a school project

I'm wondering if After Effects can help me do a project for school.

I'm going to record a video of me holding a set of cue cards, and going through them one by one while I speak on camera in a sort of presentation. As I go through the cue cards, I'd like to embed some YouTube videos that I've downloaded onto the face of particular cards in the set. So as I speak in the video, I show a new card, and the video is "playing" on the new card that I've exposed in my presentation. I then pull a new card out and there's a different video "playing" on the face of that card.

Can anybody help me? Is it even possible? I'm sure it's possible. But, the question is, is After Effects the right tool? If not, can you point me in the right direction?