I use APT on a netbook along with all other astro programs: Gemini ASCOM; PHD; image viewer etc.
You
don't need great processing power to run a telescope rig and taking images.
You
do need a lot of processing power if you plan to manipulate images on the PC.
I suggest a netbook for telescope work that has a long battery life and a 1366 x 768 native resolution (looks better on the eyes) minimum. Although I use a 11" screen ACER I find it a tad small so a 13" would be better. though this will cost more and have less battery life! The only good thing about my Acer netbook is the screen resolution (Size) and 6 cell battery (long battery life) 5+hrs.
I
do not recommend ACER brand though!

..don't get me started on that!
Oh and plenty of USB ports as well...