1. CPU architecture is more important than CPU speed. That is, a Core i5 is better than a Core i3, even if the i3's clock speed is faster. Avoid the bargain basement CPU's like Celeron's, Duo's, Atom's, etc. If you stick to the Core i3/i5/i7 lines, you are pretty safe.

2. There's a few brands that I tend to avoid (Lenovo, Acer), but otherwise most brands are fairly comparable. But I do tend to prefer the "business" class laptops to the regular consumer class laptops -- the physical construction is usually a bit sturdier. With Dell, for example, you would want to look at the Latitude series (business class) rather than the Inspiron series (consumer class). But that's just a guideline -- there are plenty of good consumer class laptops as well.

3. Memory and hard drive size aren't very important, unless they will be doing specific tasks like video-editing or something like that with huge file sizes. 8 GB of memory would be good safe number. Easy to upgrade memory later if needed. Most laptops come with several hundred GB of hard drive storage, which is quite a bit.

4. The big new thing in laptops right now is using an SSD (solid state disk or drive) rather than a conventional hard drive. An SSD uses memory chips instead of magnetic platters for storage. They are much less fragile, much faster, and produce much less heat than conventional hard drives. The downside is that SSD's cost more for the same amount of storage. If the choice comes down to one laptop with a smaller SSD and another with a larger conventional hard drive, I would choose the SSD every single time.

5. The screen, the keyboard, and the trackpad are the three things you actually interact with -- if you have the option, try to compare laptops in person so that you can get a feel for those things. Sometimes a poor screen or keyboard can ruin an otherwise good laptop.