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While it's often hard to define exactly what is the very first of some particular technology, I believe many people claim the PDP-1 was a minicomputer and thus would trump the LINC and PDP-5. Though probably the actual term "minicomputer" was not yet invented when the PDP-1 was introduced. It was of course physically larger than the 8 or 11 due to the available technology, but architecturally of a similar size. It was also quite inexpensive compared to other computers in the late 50s. Larsbrinkhoff (talk) 10:05, 9 July 2019 (CEST)

In a way, yes; it was definitely intended for use by a single person (which was a hallmark of early minis), but .. all the first computers were intended for use by a single person, and later minis were timesharing computers.
There are three axes to measure 'size' on; physical, capability, and cost. The latter was a key one as it enabled small units within a larger organiztion to have 'their own' computer, as opposed to relying on a gargantuan one controlled at the top organizational level. I don't recall where the PDP-1 was on the latter, but I suspect it was still not 'cheap'. Jnc (talk) 13:37, 9 July 2019 (CEST)

Medium size

I have seen 60s literature refer to "medium size computers". This seems mostly forgotten today, with only mainframe and mini categories being in use to describe machines of that era. But it seems a useful distinction between a mini which is just a cabinet or a few boards, and a hulking room-sized mainframe with a plethora of subordinate I/O processors. Larsbrinkhoff (talk) 09:59, 9 July 2019 (CEST)