Looking for a parts for a $600 PC build?

This summer I would hopefully be able to build a PC. I can only dedicate 600 to the tower and OS. Then after that I will buy a monitor. Honestly if you suggest parts, don't worry about going over by that much. My max budget for the PC without monitor is probably like $620. I'd like a PC that can run games like Skyrim, and Battlefield on good graphics, not ultra, but I'd like better than just decent. The main reason I want this PC is to Play Minecraft on good graphics, with maybe a mod pack or so. Also I'd like to do some PC recording on Minecraft. Also I'd like to be able to use my Elgato for my Xbox.

For processor, go for an AMD FX-6000 or 8000 series processor. For motherboard, get something with AMD 970 chipset.
If you want to overclock, get an aftermarket cooler. The Cooler Master Hydra 212 Evo has gotten very good reviews and ratings out performing other coolers costing up to $80 or so while costing but $29.
1tb HDD - $55-$60.
DVDRW - $23
8 gigs RAM $70-$80
Decide what type of case you want and what size. If you want a mid tower, I recommend the Enermax Ostrog series. For $50 they have some really nice features, such as top mounted USB ports and a handle built in the top of the case.

Graphics card… What ever you have left over… Pick the best performing card you can afford on the following chart:

http://www.futuremark.com/hardware/gpu
Once you have determined all the other parts, go to a site like
www.thermaltalke.outervision.com and enter all of your component information and it will tell you how much power you need. Add 100 watts or more to that number to provide for future growth. Be sure to purchase a supply that is 80+ Bronze or better certified.

I don't think you can keep within your budget, as a good video card and power supply will chew it up.
Get the specs for the games you want to play.
Select the best hardware requirements from the lot. And consider buy better because you don't want to be too far behind when the new series of games come out.
EXAMPLE:
You Do need a machine that meets these requirements for Skyrim.
Recommended
-Windows 7/Vista/XP PC (32 or 64 bit)
-Quad-core Intel or AMD CPU processor
-4GB System RAM
-6GB free HDD (Hard disk drive) space
-DirectX 9.0c compatible NVIDIA or AMD ATI video card with 1GB of RAM: Nvidia GeForce GTX 260 or higher; ATI Radeon HD 4890 or higher
-DirectX compatible sound card
-Internet access for Steam activation

I would recommend the fx-8320 or the 8350 because they have 8 cores and that is good for gaming. I myself have the fx 8320. The r9 270x is very good for its price. The sapphire r9 270x dual-x oc edition 2gb gddr5 is about 170-80 dollars, but that's fine because most of your money should be spent on the graphics card. 8gb of ram should be enough, and the 1866 speed is optimal. The asrock 970 pro3 r2.0 is a very good, because it has all you need. It has 6 sata ports and it has usb 3.0 support and it also has 4 ram slots, so you can have 32 gb of ram maximum. The hdd is up to you, but i recommend 1tb because you should always overestimate the amount you will need. The psu will need to be 500w if you are running the r9 270x (which i highly recommend, because i have it and i can play bf4 ultra, as well as skyrim. The optical drive is necessary, but i doubt ou will need a fantastic one, so get a cheap one.