If you want just to play I would start with a desktop system. Sometimes, the laptops can have problems at installation due to the implementation of their design towards power efficiency. Theoretically, a desktop is a safer bet. Also, since proper power management on linux with laptops takes some hacking on many laptops in order to work properly, you will have less running time on batteries if this is not configured correctly.
If you want just to play and try linux, the safest bet is to run linux from a LiveCD distribution such as Ubuntu or Knoppix. This way the operating system on your hard drive stays intact and you get to play with linux. Usually these distributions also have an option to install on the hard drive.