Building your own isn't about saving money. It's about spending the same amount of money and ending up with a much better system.
If you think that you'd have to spend MORE to build your own system, then you don't know how to pick components. At worst, if you shop carefully, you will save a little money if you build your own system. At worst. It often works out about something like this...
Pre-built system $1300
Custom build $1250 (with better power supply, better motherboard, better graphics card, etc.)
But whatever your budget, you will find that you can build a better system for the same amount of money...or a little less. Except at the extreme low-end. But you won't be gaming at the extreme low-end.
As for installing the operating system, drivers, etc...
You will spend a LOT more time and effort setting up a pre-built system. This is because pre-built systems come loaded with many GBs worth of crapware, ad-ware, trial-ware, spyware and other bloatware. If you carefully get rid of all the crap, it might take you weeks to get it all working right.
With a custom build, you install only the software you want. It's time-consuming, but it's easier and faster than trying to clean out all the garbage from a pre-built system, by far!
If you are into gaming at all, you have to build your own. Buying pre-built means you get a massively crippled system....or you over-spend by a few hundred dollars OR MORE. That is, if you can find something decent for gaming, which is tough to do if you want to buy something pre-built.