Placed a pre-order for Diablo 3 <.<;;

If the beta I played is any good as an indicator then I don't actually have a computer that would be able to run the game smoothly right now. My laptop is decent when it comes to power but of course the video card forms a bottle neck. My tabletop computer is at my student apartment, some 400 km west from my current location and I have no idea when we'll be able to go there to get it. I suppose I could steal BF's computer for a while, depending on the DRM on the game. I don't have any recent experiences with Blizzard games so I have no idea what they usually do by the way of protecting their games from piracy. As I understand it in most extreme cases you can only install a game once and after that you need to contact customer support and convince them to give you a new activation key. I don't know. As a regular customer of GOG.com and only having purchased games made by CD Projekt RED these last years I feel like I'm some sort of pampered princess and I have no idea what the realities with DRM are these days. I only hear the horror stories.

So can anyone tell me, is it realistic to expect that I can install a game on one computer and play it and then change to another computer without any problems or extra steps on the way? Remember to use simple words so that an unrepenting console gamer like me can understand too :D