Here's information on the motherboard. http://www.asrock.com/mb/Intel/Z97E-ITXac/ Check the M2 slot. It takes 30mm and 42mm M2 cards. Does that work for you?
The stock cooler that comes with your CPU will do for ordinary 4-6 hours a day 'business' use. If you plan to have it running 24/7 while it processes data, I would consider a better aftermarket cooler, which is always much easier to install at the time of construction.
No, that small case will not do. You computer will need well over 100 Watts of power and the power delivery for that case is too low. In addition, your system will be using the Intel stock CPU cooler at least.
The motherboard and cooler will fit in the Lian Li case, but the 3.5" 2Tb HDD will not. If you like that style, you will need to move up to the TU200 case.
The SFX Silverstone Strider is the PSU I use in this system and I am very satisfied with it. I'm using the larger Silverstone Milo ML07 case, a slim HTPC case that was featured in the first of the builds in my post above.
Here's the current build.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Xeon E3-1246 V3 3.5GHz Quad-Core Processor ($276.99 @ SuperBiiz)
Motherboard: ASRock Z97E-ITX/ac Mini ITX LGA1150 Motherboard ($121.98 @ Newegg)
Memory: G.Skill Trident X Series 16GB (2 x 8GB) DDR3-2400 Memory ($107.89 @ OutletPC)
Storage: Samsung 850 Pro Series 512GB 2.5" Solid State Drive ($219.82 @ Amazon)
Case: Lian-Li PC-TU100A Mini ITX Tower Case ($95.99 @ SuperBiiz)
Power Supply: Silverstone Strider Gold 450W 80+ Gold Certified Fully-Modular SFX Power Supply ($88.99 @ SuperBiiz)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($93.75 @ OutletPC)
Total: $1005.41
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-07 05:27 EDT-0400
It lacks the HDD. You need the TU200 case, which is similar, to fit a 3.5" HDD, but you may be able to fit a slower 2.5" HDD.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Xeon E3-1246 V3 3.5GHz Quad-Core Processor ($276.99 @ SuperBiiz)
Motherboard: ASRock Z97E-ITX/ac Mini ITX LGA1150 Motherboard ($121.98 @ Newegg)
Memory: G.Skill Trident X Series 16GB (2 x 8GB) DDR3-2400 Memory ($107.89 @ OutletPC)
Storage: Samsung 850 Pro Series 512GB 2.5" Solid State Drive ($219.82 @ Amazon)
Storage: Western Digital Green 2TB 2.5" 5900RPM Internal Hard Drive ($128.99 @ Amazon)
Case: Lian-Li PC-TU100A Mini ITX Tower Case ($95.99 @ SuperBiiz)
Power Supply: Silverstone Strider Gold 450W 80+ Gold Certified Fully-Modular SFX Power Supply ($88.99 @ SuperBiiz)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($93.75 @ OutletPC)
Total: $1134.40
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-07 05:29 EDT-0400
Since you have a Z97 overclockable board, I upped the memory to 2400Mhz. You will be able to use that with the Xeon and it will give you around 10% speed increase for computational tasks, but it is a place to save money, if the budget is getting out of hand.