For a modest Plex library, the cheapest suitable mini PC may be better than a workstation. The deciding questions are whether your clients can play files directly, whether the server must convert video, where the media files live and whether you also intend to run virtual machines or fast network storage.
Beelink Mini S13: a small media-server starting point
The Mini S13 listing combines an Intel N150, 16GB RAM and a 500GB SSD. Intel confirms that the N150 supports Quick Sync Video. That is relevant if Plex needs to convert a video for a client that cannot play the original format. Plex says hardware-accelerated conversion requires a Plex Pass and compatible settings. It does not mean every file, subtitle format and client will behave the same way. Direct playback avoids conversion entirely when the client supports the file.
The 500GB internal SSD is more appropriate for the operating system and server software than for a large film library. Plan separate storage and backups. A USB drive or NAS can hold media; neither becomes more reliable merely because it is attached to a mini PC.
Beelink Mini S13 (Intel N150, 16GB/500GB)
Processor: Intel N150
Graphics: Intel integrated graphics
Listed configuration: 16GB DDR4 / 500GB SSD
MINISFORUM MS-01: for a broader home lab
The MS-01 has a Core i9-13900H, two 10Gb SFP+ ports, two 2.5Gb Ethernet ports, three M.2 slots and a half-height PCIe expansion slot. This hardware is appealing if one box will host virtual machines, network services and fast storage as well as a media library. It is harder to justify solely for a few Plex streams. The 10Gb ports need compatible SFP+ equipment and a network that can use them; they do not speed up a 1Gb switch.
MINISFORUM MS-01 (Core i9-13900H, 32GB/1TB)
Processor: Core i9-13900H
Networking: 2× 10Gb SFP+ and 2× 2.5Gb Ethernet
Listed configuration: 32GB DDR5 / 1TB SSD
Buy for the storage and network you will actually use
Check the total cost of the server plus disks, enclosure or NAS, backup storage, and any Plex Pass subscription. The N150 is a compact entry point when media already lives elsewhere. The MS-01 suits someone who can name the extra network or expansion capability they need. Neither replaces a multi-bay NAS automatically: think through drive redundancy, backups and how you will recover the library if a disk fails.