Do you have to get a notebook? You can get a lot more bang for your buck with a desktop workstation.
For the benefit of folks who couldn't click on the link, it's an Asus laptop running an Intel Pentium N3540 processor (4 cores running at 2.16 GHz with a 2 MB cache), 8 GB of RAM, a 1 TB notebook hard drive (running at 5400 rpm), and an integrated Intel graphics processor (i.e. not a dedicated GPU).
With only 8 GB of RAM (the minimum to run AE), I would suggest not running any other apps while you have AE going. That's a pretty slow processor too. You won't ever be able to use some third-party plugins (like Element 3D or Red Giant Universe) because they run on a dedicated GPU and that machine doesn't have one (and you can't add one later). A desktop, on the other hand would get you more bang for your buck now and be able to be upgraded in the future.
There are two things you might be able to upgrade on that laptop down the road: RAM and hard drive (a solid state drive makes a big difference and so would doubling the RAM).
So, to answer your question, a simple AE project would work acceptably (as long as it doesn't involve certain 3rd-party plugins), but I wouldn't recommend having Illustrator or Photoshop open simultaneously and you should really consider a desktop.
Moved to the Hardware forum.