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When I learned Special Relativity, it was taught in terms of basic linear algebra, without any mention of the Minkowski space, proper time as integration on the metric, etc.
However, when I am trying to learn General Relativity from several books (Wald, Carroll, Weinberg), it seems they all assume I am already familiar with SR and Minkowski space, and only briefly review it.
So, I'm afraid I'll be missing some material here.
What is a good source for SR from a Riemannian geometry point of view?
For semi-Riemannian geometry in general (including some discussion of flat space) it's hard to beat Semi-Riemannian Geometry by O'Neill.
I assume you've already looked at the Wiki pages for Minkowski space, but also try this.
Lastly, Hartle's Gravity has a great introduction to relativity in Minkowski space in the first few chapters.