Strange New Worlds (SNW) is the single best entry point for someone new to the franchise, and that’s a black mountain I’m willing to die on. It blends modern storytelling with the classic Trek formula, and since it’s basically a pickup of the original Pilot, it’s pretty darn close do the beginning of the timeline.
Strange New Worlds offers an accessible entry point that holds the same core as The Next Generation (TNG) or the original series (TOS). There’s only two seasons so far, but if you like it and are craving more, I recommend watching TNG afterwards, and continuing that line in order of series air date (DS9, VOY, ENT).
It’s easy for many of us to recommend our favorite series, or our own entry points, but the reality is most of Trek is dated and not a good place to start for someone used to modern television.
The building I worked at in the Chicago loop had showers for bike commuters. Might be a big city thing.