My employer says that if I want to telecommute I have to buy my own PC. Should I get a desktop PC or a laptop?
There's no single, simple answer; here are some points to consider:
The more you'll be moving from location to location, and the more you'll be relying on one computer no matter where you are, the more you'll need a laptop.
Depending on what kind of work you do and how much you want to spend, your choice of laptop vs. desktop will be based in part on things such as keyboard size and arrangement, size and quality of monitor, CD-ROM drive availability, internal vs. external modem, and weight.
A laptop with a "docking station" might be the best of both worlds - you'll have the portability of a laptop and the full-size monitor (and other features) of a desktop.
Even though your employer says you have to buy your own computer, don't overlook the possibility of "salvaging" one from the office. For example, there might be a PC in the office that's not being used much and could get more use at your home. Or, there might be some laptops that are available for loaner use; if you only telecommute a few days a week, you might be able to borrow one instead of buying one.