If you don't play or intend playing any third-party 3D games, the graphics (GPU) will make little to no difference in most everyday basic tasks. If you have a few laptops in mind, post their links & we'll take a look & let you know which may have a slight edge over the others.
This £400 Acer Aspire 5734Z click here (Intel T4500, 4Gb, 500Gb) is good value I reckon. Have you found a similar AMD one?
What are those special features you mention about the graphics that are available only with Core ix CPUs. Do you need these features? G
P.S. With the help of this rather useful list, you can compare any laptop CPU at click here: make your choices by putting a tick next to the ones you want to compare & click on the 'Restrict' button. Ctrl + F in your browser to search for specific ones quickly (Laptops graphics comparison if needed: click here, click here &