In that case, your budget is pretty overkill, so you can consider this solid, sleek tiny build:
CPU+MB: Intel Core i3-6100 + ASRock H110M-ITX/D3 @ $298 (PC Themes)
Its high clock speed allows you to do everything very smoothly, which managed to beat Haswell Core i5 on occasions.
Its Intel HD Graphics 530 comes with the latest media codecs to let you play 4K HEVC videos in low power consumption and no hiccups, as well as decent light gaming performance similar to AMD A8's R7 iGPU so you wouldn't require another GPU.
Motherboard also comes with Intel Gigabit LAN and ELNA audio caps for best internet connectivity and audio quality.
RAM:
Kingston ValueRAM DDR3L-1600 CL11 8GB @ $45+3*
SSD:
Transcend SSD370S 128GB @ $60+3^
CASE+PSU: In Win CHOPIN BQ696 Aluminium [Silver/Black] + 150W Flex ATX PSU [80 Plus Bronze] @ $145 (AIM Resources)
Very sleek, super thick and high quality made aluminium chassis. Comparable to Apple products.
At just 3.3 litres.
However, this does not allows you to install any expansion cards such as discrete sound card or graphics card due to physical limitation.
Comes with integrated energy-efficient PSU as well.
More info: http://www.inwin-style.com/en/goods.php?act=view&id=Chopin#product_tab
OS:
Microsoft Windows 8 Professional 64-bit Product Key [OEM] @ $30 (Reddit)
Upgrade for free to Windows 10 via free Windows 8.1 update.
Total: $584
You should spend the remaining huge budget on a separate external USB based DAC for best sound isolation and an external DVD writer if you really need it since it is on its way to obsolescence.
Optional:
CPU: Intel Core i5-6500 @ +$126
If you are doing massive multitasking and opening huge Excel files with especially with macros.
MB: ASRock B150M-ITX/D3 @ +$23
If you need 2 more USB 3.0 ports.
HSF:
Jonsbo HP-400 Low Profile @ $29+3`
If you really hate stock cooler and want something slightly cooler and quieter.
Not alot of choices for this chassis at just 43cm height limit.
HDD: HGST Travelstar 7K1000 1TB [7200rpm] @ $85
If you also prefer to have some internal storage to backup your collections of videos and musics, etc...
_______________________________________________________________
OR if you prefer something more conservative with expansion options:
CPU+MB: Intel Core i3-6100 + Gigabyte GA-B150M-D3H @ $329 (PC Themes)
Motherboard also comes with Intel Gigabit LAN and Realtek highest-end AC1150 onboard audio for best internet connectivity and audio quality.
Also comes with 1x M.2 SSD slot for future expansion.
RAM:
Kingston ValueRAM DDR4-2133 CL15 8GB @ $57+3"
SSD:
Transcend SSD370S 128GB @ $60+3^
ODD: ASUS 24X CD/DVD Writer [OEM] @ $25
CASE+PSU: In Win BK644 [Black] + Powerman IP-P300BN7-2 300W SFX [80 Plus] @ $109 (AIM Resources)
A very small mATX chassis, smaller than some of the mITX chassis, and yet very high quality made.
At just 12.5 litres.
This will allows you to install expansion cards as per normal.
Comes with integrated energy-efficient PSU as well.
More info: http://www.in-win.com.tw/Corporate/en/goods.php?act=view&id=BK644 Special Edition
OS:
Microsoft Windows 8 Professional 64-bit Product Key [OEM] @ $30 (Reddit)
Upgrade for free to Windows 10 via free Windows 8.1 update.
Total: $616
You should spend the remaining huge budget on a separate external USB based DAC for best sound isolation and an external DVD writer if you really need it since it is on its way to obsolescence.
Optional:
CPU: Intel Core i5-6500 @ +$126
HSF:
Deepcool Gabriel Low Profile @ $39+3"
HDD: Western Digital Blue 1TB @ $77
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In Win CHOPIN BQ696
In Win BK644
