Budget is something that needs to be planned as it will determine what to look for and as rgd posted, a pc can cost as much as a new car. As this pc is for a student just getting into the field, you'd probably don't want to spend ~$15k.
I would recommend a desktop because they will have better performance, cost less and the more screen space, the better. Around $1500 would get a pretty high end pc with an i7, at least 8gb ram and a good graphics card like a 560ti or quadro 2000. You will probably want to go with nvidia for the graphics because some add ons use nvidia's cuda technology, especially adobe products. Multiple monitors is a big help, and I will suggest at least 2, 24" 1080p monitors. An ssd is a must for a high end build and will speed up workflow a bit. At least 120gb would be enough for the os and software. Also keep in mind the software costs quite a bit, but that can wait til which program they specifically need at the time. You will also want to get a wacom tablet, at least a medium size, or cintiq monitor if you want to spend more.
Assuming you aren't building it yourself, you could go with the major manufacturers or go with a custom build place like http

/www.cyberpowerpc.com/ which will probably offer better specs for the price. We could help pick specific parts if you choose that route. Of course we can also find a good hp/dell/etc. if you choose that route. I could post links to a few pcs but I like to have a budget so I'm not shooting in the dark.
Edit: In reply to the above post as he posted just as I did. You can't specifically look at more cores/ghz as this is not telling of performance. An 8 core amd cpu will be beaten by a quad core intel i7 even if it were less ghz.
http
/www.tomshardware.com/reviews/ivy-bridge-benchmark-core-i7-3770k,3181-15.html Also, the gpu would be more important depending on if they use gpu accelerated renderers which I would recommend doing. This will cut down on render times quite a bit.