After seeing Sailor Moon Crystal, will I miss anything by skipping the first two seasons of the original anime? I've been thinking of intermittently watching the original Sailor Moon anime (with subtitles) to get a sense of the plot (and to have something decent to watch).

Since I've already seen Sailor Moon Crystal and I've noticed that the first two seasons of the original anime seem to more or less cover the same material (and since Sailor Moon isn't a high priority series for me), I'm thinking of starting from Sailor Moon S.

If I start from Sailor Moon S, will there be any important plot points / character details that I will not know of because I won't have seen the first two seasons?

I did view the final recap episode of Sailor Moon R (and I could follow what was going on), but there wasn't enough detail that I'm completely certain I won't miss anything.
Great question!

After seeing Sailor Moon Crystal, will I miss anything by skipping the first two seasons of the original anime?

No... and yes.

No:
You are correct that Sailor Moon Crystal's 26th episode leaves off at the same point in the storyline as the end of the classic anime's R season.  If you go straight into the S season, you will not have missed out on any essential plot points, characters, or character details.

Yes: Sailor Moon Crystal is its own canon.  It follows the manga more closely than does the classic anime, but also has points where it veered away from the manga content in ways that conflict with both manga canon and classic anime canon. So there are 1) aspects of the classic anime's first 2 seasons which follow the manga in areas where Crystal did not, and 2) aspects/characters that are original to the classic anime canon and thus not covered in Crystal. The details about 30th century Crystal Tokyo differ significantly between the classic anime version and Crystal, but this will not affect jumping in from season 3 much since that material doesn't get mentioned again much from S onward. Likewise, the R season contained a plot arc that you'll have missed about the Makaiju tree and aliens who came to Earth, and the R movie contained an original story involving Mamoru's backstory, but as they are not referenced again later, you won't notice this at all. However, you will notice that some characters you met in Crystal are not in the classic anime (for example, Ittou Asanuma is absent from the classic anime until a tiny cameo in season 5, whereas Kumada Yuuichirou is a love interest for Rei original to the classic anime starting in the 1st season). So there will be moments where you'll notice things like, "I guess I'm supposed to know who this person is," or "I see that Mamoru actually transforms by magic into Tuxedo Kamen in this version," etc.

Recommended: Watch the first episode of the classic anime, then watch episodes 8, 10, 25, and 34 (the first appearances of Ami, Rei, Makoto, and Minako) so you can meet them in their classic anime personalities (Ami and Makoto are pretty similar to how you know them, whereas classic anime Rei and Minako are fairly different in personality from the personas given to them in Crystal). Then jump ahead to episode 90 (a.k.a. episode 1 of the S season).