"Most" is incredibly vague here. Overclocking that Pentium should help, but you need a better motherboard. I mean this would handle some basic stuff like Fallout 3/NV, Elder Scrolls 3-5, Counter Strike GO, TF2, and some other stuff at 1080p but probably medium settings for 60FPS.
It's better to build around the games you want and like to play but leave room for upgrading and don't be afraid to wait and put aside more money and to spend more money.
I started with a build similar to this a few years ago of course I used a 7870(the R9 270x is just a renamed 7870) and an i5 3570k (which I've since overclocked nearly an entire Ghz over stock and still use since I don't need to upgrade and probably wont for a few years) but I've since added SSDs (no moving parts hard drive, super fast), 8GB more RAM, a 1000W power supply(for more video cards later) and a GTX 970.
Anyway here's the build:
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-4690K 3.5GHz Quad-Core Processor | $219.95 @ SuperBiiz |
| Motherboard | MSI Z97 PC MATE ATX LGA1150 Motherboard | $89.99 @ Newegg |
| Memory | Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory | $67.99 @ Newegg |
| Storage | Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive | $52.24 @ Directron |
| Video Card | PowerColor Radeon R9 270X 2GB PCS+ Video Card | $164.99 @ SuperBiiz |
| Case | Enermax ECA3253-BW ATX Mid Tower Case | $38.99 @ SuperBiiz |
| Power Supply | EVGA 500W 80+ Bronze Certified ATX Power Supply | $41.99 @ SuperBiiz |
| Total | ||
| Prices include shipping, taxes, and discounts when available | $676.14 | |
| Generated by PCPartPicker 2015-02-02 22:58 EST-0500 |
/r/microsoftsoftwareswap has copies of Windows 7 and 8.1 for less than $15 usually or you can get it for free if you know where to look. But if you want something that will have no issues with most games that build should perform fantastically at 1080p. If you want to kick the settings up to Ultra and higher I'd suggest putting another $100 or $150 into a bett Video Card. The build I posted in my other comment is good for pre-2011 games and some of today's less demanding games (anything that's multiplat with consoles you'd be able to play at console settings or slightly higher).