Minimum pc for 720p 60fps dota2/cs.go

Solution
Here you go, a very minimum build capable of playing those games just fine. Keep in mind though, that it won't run anything else, like Battlefield 4, GTA V etc.

But Dota 2 and CS: GO, it will run 60fps + easily.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3220 3.0GHz Dual-Core Processor ($52.95 @ SuperBiiz)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($39.99 @ Newegg)
Memory: Crucial 4GB (2 x 2GB) DDR3-1600 Memory ($33.99 @ Newegg)
Storage: Hitachi Deskstar 1TB 3.5" 7200RPM Internal Hard Drive ($40.94 @ Amazon)
Video Card: XFX Radeon HD 5450 1GB Video Card ($29.99 @ SuperBiiz)
Case:...

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Here you go, a very minimum build capable of playing those games just fine. Keep in mind though, that it won't run anything else, like Battlefield 4, GTA V etc.

But Dota 2 and CS: GO, it will run 60fps + easily.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3220 3.0GHz Dual-Core Processor ($52.95 @ SuperBiiz)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($39.99 @ Newegg)
Memory: Crucial 4GB (2 x 2GB) DDR3-1600 Memory ($33.99 @ Newegg)
Storage: Hitachi Deskstar 1TB 3.5" 7200RPM Internal Hard Drive ($40.94 @ Amazon)
Video Card: XFX Radeon HD 5450 1GB Video Card ($29.99 @ SuperBiiz)
Case: Cougar Spike MicroATX Mini Tower Case ($29.99 @ Mwave)
Power Supply: EVGA 430W 80+ Certified ATX Power Supply ($32.99 @ SuperBiiz)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($12.99 @ Newegg)
Total: $273.83
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-08 05:58 EDT-0400

EDIT: Ooops forgot monitor, though basically anything is fine. Just get a cheap 22/24" monitor. :)
 
Solution
Here ya go:

Intel build

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor ($108.99 @ NCIX US)
Motherboard: Gigabyte GA-B85M-GAMING 3 Micro ATX LGA1150 Motherboard ($47.98 @ Newegg)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-1866 Memory ($51.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: Gigabyte GeForce GTX 750 Ti 2GB WINDFORCE Video Card ($109.99 @ Newegg)
Case: Cooler Master N200 MicroATX Mid Tower Case ($34.99 @ Newegg)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($19.99 @ Newegg)
Monitor: Acer S220HQLAbd 60Hz 21.5" Monitor ($99.99 @ Amazon)
Total: $523.91
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-08 06:05 EDT-0400

AMD build

PCPartPicker part list / Price breakdown by merchant

CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($69.99 @ NCIX US)
Motherboard: ASRock FM2A88M PRO3+ Micro ATX FM2+ Motherboard ($48.98 @ Newegg)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-1866 Memory ($51.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: Gigabyte GeForce GTX 750 Ti 2GB WINDFORCE Video Card ($109.99 @ Newegg)
Case: Cooler Master N200 MicroATX Mid Tower Case ($34.99 @ Newegg)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($19.99 @ Newegg)
Monitor: Acer S220HQLAbd 60Hz 21.5" Monitor ($99.99 @ Amazon)
Total: $485.91
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-08 06:04 EDT-0400

If you want to upgrade the GPU, you will need to upgrade the PSU, but for the budget this is pretty good.