First of all you will need to decide what style and size of computer casing you will be purchasing. Your options are either a tower casing or a design top casing design. Most computer casing today will come as default tower casing as they take up much less space compared to the desktop. By taking a tower you can save at least 50% space on your desk.
Once you have chosen the tower casing you will need to consider whether you want a small mini, medium midi or the larger full tower. After that you will need to see whether you want a small mini tower which is small and compact but will lack the room for a lot of hardware.
Or you can look at a midi tower which is the choice of most people. It will allow room for multiply hardware and still allow room for upgrades in future. Lastly you can buy a full tower but this design is normally reserved for severs of file sharing computers in your office.
So your choice by default will be a midi size tower casing as it will allow for upgrades and yet not take up much space. The sizing of the casing can be found on the companies website or in the specifications attached to the computer casing.
Two other considerations beside price and looks are the power supply and the case format. The power supply needs be suitable for intended use and the specification of the computer you are building. And the case format is generally the ATX version but some will also support the older AT format.