The learning curve to DOTP is simple as it highlights cards that are usuable & basically completes any steps that are required to cast spells for you (i.e. tapping mana). It is very simple compared to the paper version or even MTG Online as the closest thing to deck building is the ability to add certain cards to decks, instead of having a large pool of cards to choose from & building decks from scratch.
All-in-all a fun game, but definately aimed at newer players. Give the 5-minute tutorial a run through & you'll be fine.
The graphics aren't too intense, & you shouldn't have a problem with the laptop being able to run it.
Edit: I looked at your original question - Yes, the single campaign is fun as the opponents decks do actually get harder as you play along. If you're a completionist, the single player campaign will be where you'll focus most of your time too.