You do not need a top range GPU, but I would recommend a 4 core CPU (ie i7), a dedicated mid range GPU and at least 8GB system Ram.
You might get away with running a 2 core CPU, but memory will be crucial as each Everquest session uses between 500-900MB or Ram depending on models and graphics options and zones used.
I can box 8 very comfortably on a 2 year old laptop with intel Haswell i7 4700MQ and a nvidia 750M with 8GB system RAM. With care I can get it up to 10 boxes but memory starts getting low. Also, for some reason the integrated intel graphics are glitchy on the laptop, while on a similar desktop with i5-4590 I have no problem boxing with integrated graphics(both 4700MQ and 4590 use Intel HD4600 graphics, crappy but sufficient for Everquest).
I suppose the new Broadwell mobile 47W i7s with built in Iris Pro 6200 graphics would totally own, but the chips just came out last week and I am not aware of any laptops with them yet.
http://www.pcworld.com/article/2929...-and-laptops-but-world-waits-for-skylake.html
If I was buying a new laptop today I'd want one with i7-5750HQ or i7-5850HQ and skip a GPU.
Also curious if anyone has used AMD APUs for boxing Everquest.
If you are on a budget something like AMD A8 or A10 series with 2modules/4sortofcores might be sufficient. Again, GPU should not limit you in Everquest.
Oh, yeah and remember to set minimize CPU use in Options -> Display -> Advanced Options ->Max.Background FPS this setting alone cuts CPU use in half for background sessions.