I've been shopping for another laptop lately for Mrs. M8o to use, and I'll tell you... I'm kinda disgusted at most of the major manufacturers now days. Seems screen resolution has taken a back-seat to everything else lately. The
large majority of them are back to only 768 vertical resolution (sometimes even lower!) and no path to upgrade unless you get a 17" screen or larger. You hardly see any of a web page, or portrait image with that. If you're looking for a 4 or 5 lb laptop with 14" or 15" display, you're mostly out'a luck with a few exceptions; unless you get a Lenovo who seem to be an exception to this rule, and which I may be getting another one of for this reason for a thrifty $760.
Now when I was in the market a year ago, and a year before that, and a year before that, it was quite common in a 15" display to find 850, 900 and 1050 (you get the idea) vertical resolutions; or at least perhaps a 768 base, and an upgrade option to something higher. Not so much today. Blame that on your computer being "HD 720 complaint" as being something good... hey computer makers, those in the know know it's not! Some of the laptops don't even advertise, not anywhere I can find, what the resolution actually is. And I hope it goes without saying, the more screen real-estate you have, the better PP experience we RAW shooters are going to have.
So ok, that's one thing. Screen resolution. And if you're on this forum, you'd probably be happiest having the highest rez you can have.
Color accuracy is right up there. But I don't have any really good way of knowing which displays are the best "PP-friendly" screens. I do know my corporate issued Dell Latitude E6500 is the best screen I've ever seen; even better than on my Dell Inspiron w/upgraded 1920x1200 rez. The screen on the Latitude is the only screen I have that clearly tells me when I've over-sharpened an image. The halo created from over-sharpening "pops", and I know I need to re-do it and back-off the sharpening. Problem is I don't PP on my work-issued laptop for obvious reasons, so it's very tedious to discover instances of over-sharpening as I'm sure you can imagine, when I only discover it after the fact.
Next, of course, memory. 3 Gigs at least. If you run 64-bit, more more more.
The other thing is, CPU. Use this as a guide to get the most for your money:
PassMark Intel vs AMD CPU Benchmarks - High End PassMark CPU Benchmarks - High Mid Range CPU's
The rest is per your needs.