a 20k pc for 24x7

[d3b]

After hours of research, I'm hoping to settle with-

Gigabyte GA-H110M-S2 LGA 1151 6th Gen F20 Updated BIOS Motherboard
Intel G4560 Pentium Processor LGA1151 (3.5 GHZ,3MB Cach
Corsair Value Select 8GB DDR4 PC4-17000 Unbuffered 2133Mhz CL15 288-pin DIMM
Antec VP550P 550 Watts PS

I have a spare laptop hdd to use for now (will add ssd next month)
Now, as the mentioned mobo doesn't have hdmi, can anyone please suggest me a graphics card (with Freesync- as my previous samsung monitor supports freesync) within 5-7k

and a decent cabinet (simple and with USB 3 headers, I'm not a fan of LED lights, but something with space for extra fans) within 2-3k.
I guess I'm not missing any essential components.

And thanks for your inputs in advance.

Hypothetically, also if I could have increased my budget which one would have been better? i3 6100 or i3 6098p?

 

[nac]

If you want HDMI, get H110 S2PH

You don't need 550w PSU for this build, if you're buying this keeping in mind your future upgrade, fine.

Finding an AMD graphic card in your budget is quite tough today.

i3 have few more instruction sets than the Pentium you picked. Unless, those instructions are crucial to your work, you're good with the Pentium.