I recommend a larger budget.
I also agree with Peru Bob. A laptop that can comfortably handle Premiere Pro and After Effects will cost you at least double your intended maximum budget. At the $700 USD price point you'd be kind of stuck between a rock and a hard place: You'll get either a quad-core CPU-based laptop but with only integrated on-CPU graphics, no discrete GPU and no provision whatsoever to add one later on, or a laptop that has a very-low-performance discrete GPU (which cannot be upgraded whatsoever) but with only a dual-core CPU. And a skimpy 8GB of total system RAM (the absolute minimum that's required to run the latest releases of Premiere Pro and After Effects at all) and a very sluggish 1TB 5400 RPM hard drive are pretty much standard at this price point.