Ethernet Port Listener Throughput Maximisation
I see no problem in your case except the capacity of HDD is limited.

50 % of 1000 Mbps uplink is about 62.5 MB/s to store.
A 1 Tb HDD will be filled in full during less than 16000 seconds (about 4 h 30 min).

62.5 MB/s is not guarantied for an HDD as it write speed is about 50-150 MB/s (from here) therefore you need to parallel 2 or 3 of HDDs (e.g. RAID 0). Even low-cost Mini-ATX motherboards integrates two and more SATA interfaces.

Any modern Core-i3 PC could run that task.  You can try/test your PC with Wireshark as a software to run the packet capturing.

A LOM Gigabit Ethernet is typically OK, but if you want stronger time stamping you could use specialized capturing hardware like the Endace DAG capturing card.