First of all we need to understand what a computer desk is. Technically a computer desk is any desk which is suitable for using a computer on, so in reality so long as it is deep enough to take a screen and keyboard then any desk will do.
For the home user though, most people think of a computer desk as an all in one desk, with space for your CPU, Printer, discs, and storage space for related items, and usually fitted with a pull out keyboard tray.  Whilst these units look like the perfect solution to your needs they are a bit of a compromise for the following reasons

Firstly consider the slide away keyboard tray. They were originally designed for desks where a computer would be used for some of the time, and therefore pulled out for use only when necessary. But nowadays the computer is used for the majority of the time, which means that the advantages of a slide away keyboard is minimal, and the disadvantages become more apparent.
These disadvantages are that most extendable trays are not that rigid, so the keyboard moves up and down in use, which is very annoying.

Also there is no room to keep the mouse or pointing device close to the keyboard, which makes typing with both hands more cumbersome.

The other disadvantage is the loss of legroom caused by the under-desk keyboard tray, which makes using the computer desk less comfortable for the average person, and almost impossible for someone who is taller than average.

Also with the proliferation of wireless keyboards and pointing devices, it’s easy to just pick them up and move them somewhere else if you want to use your desk for other things than computing.

Many of the so called computer desks are fitted with slide-away keyboard trays because the desk top itself is not deep enough to place the screen far enough away from the keyboard. It is very important to get this relationship right, to prevent eye strain.

The easiest was to check this is to  sit at the desk ready to start typing on the keyboard. If you can then touch the screen with your fist the screen is too close.

The next problem with an all in one computer desk is that invariably the valuable legroom is taken up by the CPU, and possibly your printer, which means you are constantly knocking into them, and never seem to be able to find a comfortable working position. In time this will lead to fatigue and even aches and pains as you try to work, contorted around machinery fitted into a space where your legs should be.

Although it may not seem so at the time, it is far better to consider a more basic desk, 60 or 80cm in depth, with a storage unit to one side, into which can be housed your CPU, with the printer sitting on top. Nowadays you don’t even have to have the CPU and printer close to your desk, so consider if you could position them somewhere else in the room, and use extended cables or wireless connections.

You can buy an electronic unit which emulates all of the connections on the back on your computer and this can be fitted to the desk top, which makes life a whole lot easier.
If you really haven’t got space for this then opting for an all in one computer desk is about the same as fitting a double bed into a single room. It may fit, but it will look ridiculous and won’t work as a bedroom.

As always, even if it is just for one desk, measure your room and give these to a professional office furniture dealer. He should be able to plan your room using proper furniture to give you what you want, which is a proper computer desk.
You may also save some money which can be spent on a decent office chair which will make life at your computer desk even more comfortable