AMD and Intel are manufacturers of processors which are the heart of the laptop. To be frank most people won't see any difference between the two.
Ergonomics (weight/keyboard/screen), the number of USB sockets, hard disk size (and of course looks) are more relevant to the user but the most important things are the operating system on offer and then if there enough memory (RAM) fitted to run it.
The main operating system is Windows which comes in two distinct flavours at the moment Windows XP or Windows Vista. The later is the latest thing but it has received a mixed reception from many users. Vista requires more of your computer hardware especially RAM - a minimum of 2 gigabytes maybe 4 gigabytes. XP runs v well with 1-2gb. The users' reaction to Vista has caused some manufacturers to offer the option to revert to windows XP operating system which is more familiar check that option too.
The main thing is to make a checklist of what you plan to do on the laptop - any laptop can cope with standard office/home letters and web duties but any special programs for study/hobby/work will need a higher spec machine - music/video mixing and video games will certainly need extra.
As for manufacturers opinions will vary widely but most are reliable, read the reviews but above all try out the laptops in shops - you may find that one keyboard is better for your daughter than another for example. Also heck the service contracts offered, look for 2-3 years collect and return at least