This is a "naked" hard disk which is intended for internal use within a PC, server or NAS.
An external hard disk is suitable for your purposes. The following three aspects must be taken into account. 1. connector, mostly USB type A, is standard and is available on almost every PC, except the newer "Mac Book Pro" models and a handful of others which only have type C. The Mac Mini is equipped with a USB connector. On the Mac Mini, USB Type A is present on both the newer and older models, and USB Type C on the newer model.
2. storage capacity. For Time Machine backup, your Mac Mini's storage capacity should be multiplied by two. If your Mac Mini has 500GB, you should get at least a 1TB drive.
3. read/write speed. This is entirely up to you. If you need an overnight backup, a standard "mechanical" hard drive is fine. If you need a super fast backup, you should go for an SSD which is more expensive. For backup purposes, however, mechanical hard disks are superior to SSDs because they "age" relatively quickly for regular and large data streams and break down.
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