Cgminer is the simplest and most effective miner to use. That's why you should buy a AMD GPU.
Processing speed of the CPU makes no difference for mining. We just need something that can run the operating system. Plus this CPU is actually good because it uses less power.
AMD Sempron 145 Processor (SDX145HBGMBOX)
AMD Athlon II X3 455 (AM2+, AM3, 3.30GHz, Unlocked)
Arctic Freezer 13 PRO (120mm)
SeaSonic Platinum SS-860XP2 Power Supply
This is a really high quality power supply. The main benefit this has over other power supplies that are a little cheaper, is that the energy efficiency is much better than what others recommend (Being Platinum Rated). This will mean your electricity is much cheaper, and over the long run it will pay for itself.
ASUS M5A97 R2.0 AM3+ AMD 970 SATA 6Gb/s USB 3.0 ATX AMD Motherboard
This motherboard is a good choice for being cheap and able to handle the 3 graphics cards (Up to 4 actually). But you will need powered extenders.
ASUS M5A99X EVO R2 (AM3+, AMD 990X, ATX)
Just big enough for the OS. Since we are just using it for mining this will be fine.
All we need is 4gigs or so of ram. RAM has no impact on mining, we just need enough to run the OS. You might be able to pick up a stick for slightly cheaper, but this one is good and more consistently in stock.
Kingston Hyper X Blu 4 GB 1600MHz DDR3 Non-ECC CL9 Desktop Memory (KHX1600C9D3B1/4G)
Corsair XMS3 (1x, 4GB, DDR3-1333)
Riser Cables for Graphics Cards
The motherboard has 2 PCI-Express x16 and 2 1x slots. So you can go with 2 PCIE “1x-16″ risers and 1 PCIE "16x-16x" Riser or vice versa. I went with 1- x16 riser and 2 x 1 to 16 riser to reduce power usage through the motherboard. It is important for the 1x to 16x ones are powered, so that your motherboard isn’t overloaded. Risers are also necessary to help disperse heat.
Qody PCI-E Extension Cable: 1X to 16X (powered)
Micro SATA Cables - PCI-E Express 16X Riser Card with Flexible Cable
Most miners go with a simple milk crate to hold their components.
Sterilite 16929006 Storage Crate, Black
Wireless Card (optional)
Make sure the wireless card is PCI, not PCIE, so if you want to add another graphics card later, you won’t be using a PCIE slot by your wireless card.
TP-LINK TL-WN951N Wireless N300 Advanced PCI Adapter, 2.4GHz 300Mbps, Include Low-profile Bracket
TP-LINK TL-WN851ND, n300 (PCI)
I'll recommand to install a Windows 7. Everything else required is opensource.