There are really three options: Building, buying custom, buying pre-configured.
If you measure the cost of components only, generally the cheapest option is to buy pre-configured as the large companies can buy components very much more cheaply than you or I can.
Otherwise it is complete up to you based on your ability, interest, aptitude, etc.
If you have the time and the money to build your own computer, that can be lots of fun (this is me with desktops). Also, because it is unlikely that EVERYTHING in your old computer has to be replaced, it can be cheaper. You might want Super-Widget X200a but might not want Extreme-Widget X879b. So by only buying the parts you want, you can save.
If you have the money but not the time, and you really want a computer that has specific and particular components (this is me with laptops), you'll probably want to buy custom. These generally cost more, but can have pretty good warranties and allow you to have some peace of mind along with your specialized machine.
If you have neither the time nor the money nor the inclination to find out what works best together or build your own, or you really don't have any special requirements about what needs to be in the computer and what does not, then buy pre-configured. These can be the cheapest by far, and can have pretty good warranties to boot. If you're buying a computer for your parents, or recommending one to friends, and you don't want to be at their every beck and call for support issues, get one of these.
UPDATE for OPs comments:
Ok then. What you need is some explanation of what sort of hardware you ought to purchase. I recommend giving us some specific questions. Modify your question (press the Edit button below it) and add some of your specific questions that we can then address.
Money and Interest are good, but getting the knowledge necessary to build a box is no small task. It's good to do. It's probably how many of us got into computers. But it's not easy and it takes determination and persistence.
The only problem is, this site isn't very well geared towards that because what you need is specific to you more often than not. And this site tends to be better at dealing with broad issues applicable to everybody.
Websites such as MaximumPC should be invaluable at providing shopping recommendations and step by step instructions on how to build computers within a given budget. Check that out and see if any of their information helps you.