Buy right. Set it up right.
Most video cards will handle browsing. Anything you are buying should. Tearing in a browser is either
2. Flash not using dri (you can set that up in the config file)
Nvidia & ATI/AMD are the big 2. Specifically, they pack more parallel processing cores in the hardware and more usable formats in the software. Intel is coming along fast, but my hd4000 won't do OpenCL, for instance. Laptops are a special issue because most have 2 gpus using one to do heavy lifting and the other to save power. There was a Lengthy Discussion Here
, with plenty of good advice for everyone - less than 6 months back.