the IGP's performance on a notebook is not just relevant for games. If you get a notebook that has one of Intel's pre-x3100 IGPs (gma 950, gma 3150, etc), you're going to have trouble playing high resolution videos and flash content (this one is especially bothersome considering that a lot of websites use flash even if they don't have video content). 720p youtube videos are going to stutter like Lothar in front of a naked man.
AMD's E-**** series are good for your needs as they're usually put on budget laptops that fall below $500. Just bump up the RAM. Avoid AMD's older stuff (C-** models) because they run hella hot. I remember you're having issues with heat.
As for build, I have no idea. Most of the laptops that I have owned seem plastic-y and frail to the touch. Except the Dell Latitude, which I believe was the point of the product line (Inspiron - home use, frail. Latitude - business use, rugged, and very gay.)