Your description of the games that you'd like to play really vary in how hard they impact your computer, so I'm going to suggest this build to you that I've created and given to every one of the people that have asked for a build on this budget, and maybe it could suit you. This is just a slight dollar over your current budget, but borrowing a few dollars from your parents couldn't hurt.
CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor
Motherboard: ASRock H81M-HDS Micro ATX LGA1150 Motherboard
RAM: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive
Graphics Card: Asus GeForce GTX 760 2GB DirectCU II Video Card
Case: Enermax ECA3253-BW ATX Mid Tower Case
Power Supply: Corsair CX 430W 80+ Bronze Certified Semi-Modular ATX Power Supply
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer
Operating System: This is all personal preference and what you know the most, but either Microsoft Windows 7 Ultimate Full (32/64-bit) or Windows 8.1 (32/64) would do.
The GTX 760 in this build is what I used for about 7 months, and it almost did better performance wise than my GTX980 that I have currently.