[Build Help] - Looking for a CPU + Motherboard to upgrade current build

Hi Im Looking for a CPU and Mainboard to upgrade the computer of my brother.(Because his MB is defect and its not possible to buy a cheap one with a socket which is not in production anymore.)

• Main purpose : Gaming, Video Rendering (Non professional)

• Parts of the actual build (Don´t worry for the PSU).

• The price should be between 200€ and 300€ (Preferred from Amazon)

so far, so good.

My favorites for the given purpose and build are:

• Intel BX80646I54590 Core i5-4590 Prozessor (Sockel 1150, 4x 3,3GHz)
• Gigabyte H87-HD3 Mainboard Sockel LGA 1150 (ATX, Intel H87, DDR3 Speicher, 6x SATA III, HDMI, DVI, 4x USB 3.0, 2x USB 2.0)

Im looking forward to your recommendation and suggestions.

KR, Phips