Ed,
I would start at the very beginning to understand their roots and how they helped establish a genre. That would be the Speak & Spell album from 1981. Just Can't Get Enough being the hit a top hit. Founder Vincent Clark leaves the band after this album (see Yaz/Yazoo). Sound quality is a bit typical of 80s CDs--poor.
Alternatively, you could get The Singles 81-85 a compilation album. It highlights the seminal DM sound. Synthesizer lead, with strong pop hooks some early industrial. I have 3 of their "best of" albums and this is the best of the older material from a sound quality perspective.
I find Music for the Masses a classic. The songs range from experimental, dark, introspective, minimal sounds, to choral. When you've finished listening you have something to think about. My second top DM album.
To me Violator was their last album with their signature sound, while guitar comes out from the background to mix things up. This album it is well connected, consistent and solid. I feel it has the most number of accessible songs to date.
Songs of Faith and Devotion is the start of a divergent sound for DM, they use much more raw guitar and dropped the heavy synth keyboard. There is an underlying tone of turmoil tension confusion in the music. It is soulful and uncharacteristic. Though as much as I like the classic DM, this is likely my most played DM album in the last few years.
I have most of their newer albums but they don't get a lot of play time; just a couple of cool songs on each.
Also consider renting/streaming their movies: documentary: Depeche Mode - 101 movie, and Depeche Mode-videos, for even more exposure.
cheers, ed
