SHopping for a laptop

I'm in the market for a new laptop. My wifey has imposed a rock-bottom price limit. The PC I'm replacing is a Dell Inspiron 13" laptop with a core2 duo with 2 GB of RAM. It is barely able to run lightroom 4.

I'm not going to get a fast computer, (It vexes me greatly) but I want to be certain that I'm not taking a step backwards and I really don't know a thing about how processors have been improving in the past 4 or 5 years. I buy a computer every... 4 or 5 years and I don't read about them.

So for the money I'll be spending, it looks like it's going to be a core i3 or an AMD A4. I'll be stuck with on-chip graphics processing. No budget for an add-on graphics card. In the little bit of reading I've done, I see that the i3 is the clear winner for raw processing speed, but it looks like AMD has a slight edge for on-chip graphics processing. Is that an advantage when running lightroom? Is one or the other clearly better if my most intensive task is raw processing in LR4?

How about a difference between 4 and 6 GB RAM?

Just trying to get an idea of the best place to spend my very limited funds. Thanks for your input.

-Carl