The 5e Rising from the Last War is by far the best introduction to the setting. It is very focused on delivering the practical information you need: what are the key differences between Eberron and traditional fantasy settings, what are the interesting features of each region and faction, what you should think about when making a character from a particular nation, etc. Exploring Eberron from the DMG is also very good, although that is the only other book I own for 5E.
3E has the most material (12 hardback setting books), so if you want a deep dive, that is where you should look. It is a lot of material, and much of the later stuff was not done by the original authors of the setting so the quality is a bit uneven.
Honestly, there is not a ton of differences between the lore in the editions, other than the 4E version squeezed dragonborn and tieflings explicitly into the setting. Unless you are really hung up on only having one edition, I would get Rising from the Last War to start, then pick up some of the 3E stuff to fill in specific gaps: so if you are running a Xen'drik campaign, get the 3E Stormreach and Xen'drik sourcebooks.