If you are getting one computer for you and your family to use then you need to consider what the specific needs of your family are, and what the computer is most likely to be used for. There are pros and cons of both. There are 4 main issues:
•    Do you need to move the computer?
If different people are going to use the computer in different places say, a bedroom, the kitchen table, out of the house to use somewhere else for example, then you will need a laptop. If young children are to use it the machine should also be robust and preferably used on a stable worktop. The floor or a wobbly coffee table are probably not a good choice.
•    Are you short of space ?
If, in between using the machine you will need to put it away, or the places where you can use it have limited space you will also do better with a laptop.
•    Will someone be working at the computer for long periods of time?
In terms of ergonomics, that is, that is, the design of a safe and comfortable workspace, then the desktop is a much better option. It users are likely to spend long periods of time working on your computer then the computer desk and or workstation has to be set up to minimise eye strain, strain on the neck or back though incorrect posture and of repetitive strain injury due to excessive strain on the wrists and fingers. It is fairly straightforward to do this for a desktop, but very difficult for a laptop. Most people do not bother to set up an ergonomic workstation for their laptop as it requires another keyboard and a fixed workstation (which may defeat the purpose of buying a portable anyway.)
•    Have you a limited budget ?
Laptops, having to have their technology in a smaller space tend to be more expensive, and if the family is mainly going to use the machine for the internet and wordprocessing  a laptop would be a good choice. However, if the computer is to be used for video games, functions such as video editing and desktop publishing then these require additional memory and storage and perhaps better sound and video cards. These extras will add considerable to the cost of a laptop.

If it is a first purchase for the family then it is wise to look around and take advice before making a purchase as well as making sure what each member the family thinks they want to use it for.