Good gaming rig on budget?

I've decided that i want to build to build a gaming rig within a budget of 600-700$. So i went on memory express (memoryexpress.com) to start searching for parts (which is the computer store in Edmonton, Alberta) and i came up with this list. Please let me know if these parts are capable of playing games like minecraft (Heavily modded), TF2 and possibly skyrim. If you have any ideas of what would fit better in this rig that stays within my budget please let me know!
Thanks

List:

Case: Silverstone precision PS08 Micro-ATX Case
Cooling: ARTIC F12 Rev. 2 PWM Fan, 120mm
Memory: RipjawsX Series 8GB PC3-12800 Dual Channel DDR3 (2x4GB)
Motherboard: MSI FM2-A55m-E33 w/ DDR3 2133, 7.1 Audio, Gigabit Lan, PCI-E, CrossfireX
Processor: Intel i3-4330 Processor, 3.50GHz w/ 4MB Cache
Power Supply: Silverstone Strider Essential 700W Power Supply
Hard Drive: 750GB Blue SATA III Notebook Hard Drive w/ 8MB Cache
Graphics Card: Radeon HD 7750 Core Edition 1GB PCI-E w/ DVI, HDMI, DisplayPort

Thanks Again
Be sure to let me know if what I should change
Liam

Added (1). Case: $39.99
Cooling: $6.99
Memory: $89.99
Motherboard: $44.99
Processor: $159.99
Power Supply: $79.99
Hard Drive: $69.99
Graphics Card: $129.99
Mouse: $14.99

Total Price: $636.91

Your build is great except for one glaring flaw: your CPU and motherboard aren't compatible! That motherboard will only take AMD APU's, not Intel processors. Here are my suggested changes:

Motherboard: MSI H81M-P33
This motherboard is compatible with the i3 you have listed, and gets you everything you need at a good price.
http://www.memoryexpress.com/Products/MX48196

Hard Drive: Western Digital WD10EZEX.
It has more storage space, accesses data faster, and costs the same as the laptop hard drive.
http://www.memoryexpress.com/Products/MX40551

Graphics Card: Asus R7250X-1GD5
This card's a little faster then the HD 7750 you have listed, and costs the same amount.
http://www.memoryexpress.com/Products/MX50498

Power Supply: EVGA SuperNOVA NEX750B
This power supply supplies more wattage than the Silverstone Strider, and it's semi-modular for better cable management. It also costs $10 less after rebate.
http://www.memoryexpress.com/Products/MX47436

I wouldn't get another 120mm case fan, as the Silverstone case only has one 120mm mount that's already occupied with a fan from the factory. Without the fan, the grand total for my modified build + mouse is $630.