Cost effective way of PC Gaming is to get more and more familiar with a PC. For that reason I recommend finding a store that builds computers.
Also recommended to know how to install windows, troubleshoot, install and uninstall software such as 1 antivirus and so on...
HP Compaq, Gateway, Dell and so on are real cost effective on PC's I look down as Crap. To be fair they are PC's that use the bare minimum, they sometimes come down to cheaper then my own cost of build yet it shows in quality. Those are fine solutions for company workstations or a computer just used for microsoft office and internet.
If a brand name computer has a videocard or any upgrades, it will be overpriced and most of the time the components inside such as Motherboard or PSU are of terribly poor quality.
My recommendation would be to find a local computer shop such as Microbytes or better yet a friend or family friend or "That Guy" and have them build you a PC with specs recommended by this forum.
Such as
Phenom2 945
2x2 DDR3
Asus M4A785
Case with minimum 500W Psu by Antec or Thermaltake
Radeon 4850 or Nvidia 250GTS
500Gig HDD
DVDRW...
Windows 7 License to save the trouble.
Avira Antivir Free
That PC installed by "That Guy" will have a clean performing OS. An HP will have so many trial software to remove that ... well kill the feel of a new fresh computer.