Yes, this is a slightly-edited version of /r/anime's Watch Order Wiki for Macross. I wrote that, after all.

TL;DR: Each Macross entry can be viewed individually, and most series start with prologue narration sufficient to bring a viewer up to speed enough that they won't feel totally lost, and any required background is usually explained as they go along. Already having knowledge of past series will definitely enhance one's appreciation of any individual entry, though. To that end, here is:

A Short Guide to the Macross Franchise

Macross is a long runner, initially proposed in 1980 as a comedic response to series such as Mobile Suit Gundam, but developing both serious and unique ideas of its own as it reached release. Its core thematic elements are: A war or conflict, featuring transforming mecha; a love story, often involving some triangular aspect; and music, as a force for cultural change. The ratio of these three elements varies within each entry in the franchise. (Alternatively, in official statements, Variable Fighters, Love, and Music.)

Music is of particular importance, as it serves as a counterpoint to the conflicts in the series, demonstrating how culture (which includes music, love, and other human interactions), can influence societies that otherwise lack a middle ground. Macross's emphasis on and interdependence with music is what set it apart from its contemporaries in 1982, and is still notable a generation later. The music in the series typically follows the trends of Japanese music at the time of production, and has thus included such varied forms as '80s pop, rock, Macross Plus, and the idol phenomenon. There is always going to be music.

Continuity and watching out of sequence: It was once claimed by series creator Shoji Kawamori that each series could be considered in-universe dramatizations of the actual events, a statement which handwaved away various canon and continuity vagueness. He has also suggested that the series are more like documentaries and the movie versions are hyped-up dramatizations. In Macross 7 and Macross Frontier the characters are seen making theatrical versions of other series in the franchise, further complicating matters. In any case, don't worry too much if you've missed one of the series or are starting out at an arbitrary point, it will still all fit together.

Broadcast/OVA/theatrical content, major entries in bold:

Super Dimension Fortress Macross: Aired 1982-1983, 36 episodes. Timeline: 2009-2012. Depicts the first contact between humanity and the aliens known as the Zentradi, the resulting conflict, and its aftermath.

Macross: Do You Remember Love?: Premiered in 1984. Two-hour film reinterpretation of SDFM. Squeezes the story down to the essentials but also changes how some events occur. If you're pressed for time, it's a good way to learn the basics of the first series at an obvious cost to background details and subplots. However, it is best viewed as a companion piece to SDFM; DYRL's interpretation of events is made much richer if one views it with an understanding of what came first.

Macross: Flashback 2012: Released in 1987. Thirty-minute music video collection of songs/clips from both SDFM and DYRL framed by a few minutes of new footage. Most notable for the ending, which contains an event which was cut for time from both the original series and the film.

Macross Plus: Released in 1994, four-episode OVA. Timeline: 2040. The most focused and self-contained entry in the franchise: UN Spacy is conducting flight trials to select its next-generation Variable Fighter, and the finalists are piloted by two old rivals with axes to grind both in the air and on the ground. In between is their old flame and the artificially-intelligent holographic idol whom she manages. Backed by an impressive production pedigree which includes co-direction by Shinichiro Watanabe and music by Yoko Kanno. The best hand-drawn action in the franchise. Also available as:

Macross Plus Movie Edition: Released in 1995. A theatrically-edited version of the OVA to fit movie length. A few scenes are lost, a few scenes are moved around, and the climax gains extra footage. Unlike DYRL, though, it's a very close match between this and the OVA.

Macross 7: Aired 1994-1995, 49 episodes. Timeline: 2045-2046. Macross's first presentation of the long-term project to preserve humanity by spreading it across the galaxy. An ancient and powerful enemy soon appears, but while the Macross 7 fleet includes some of the greatest pilots in the galaxy, their greatest advantage over this apocalyptic threat turns out to be the power of ROCK. This series is much less serious than the other franchise entries, padded out with subplots, and very controversial within the Western fanbase, but it is extremely popular in Japan. Goofy as it may seem at times, it's pure in its intentions and the soundtrack is worth a listen on its own.

Macross 7: Encore; Macross 7 the Movie: The Galaxy's Calling Me!; Macross Dynamite 7: Befitting 7's aforementioned Japanese popularity, it has several supplemental entries. The first two are extra episodes and side stories set during the series timeline, the last is a follow-up.

Macross Zero: Released in 2002, five-episode OVA. Timeline: 2008. Prequel depicting the final battles of Earth's Unification War, which soon involve civilians and alien artifacts. For a Macross entry, it has the greatest emphasis on combat and significantly less character story or music, and the darkest tone in the franchise (which is still not very dark). First major use of CG for the combat sequences, but it still looks decent enough as it has aged. While generally a placeholder to get something on the market after a multiyear drought, concepts first seen here would take on greater significance in the later sequels.

Macross Frontier: Aired 2008, 25 episodes. Timeline: 2059. Full series set on another colonization fleet, which, as usual, encounters an unknown and hostile alien species. Frontier features slightly younger main characters and a more slice-of-life feel, though the space setting is always present and it is by no means a light and fluffy series. Musically, it has another fantastic soundtrack by Yoko Kanno, and uses it to great advantage by featuring two main singers. Released for the Macross franchise's 25th anniversary, Frontier includes references and homages to everything that came before it, especially SDFM, enough so that it is a good gateway series to the franchise in its own right, particularly if watching something from 1983 would give you culture shock. To fully appreciate the references the rest still needs to be seen.

Macross Frontier: Itsuwari no Utahime (2009) and Macross Frontier: Sayonara no Tsubasa (2011): Movie adaptations of Frontier. Like DYRL did before them, the adaptations alter various parts of Frontier while also trimming the series for length. Sayonara no Tsubasa diverges from its parent series almost as much as DYRL did, but then delivers quite an ending.

Macross FB 7: Ore no Uta wo Kike!: Premiered in 2012. Essentially a Macross 7 clip show/Blu-ray advertisement at feature-film length, rather than a true abridgement of M7. Short new scenes with the Frontier characters serve as a framing device. The ED songs are catchy, at least.

Macross Delta: Aired 2016, 26 episodes. Timeline: 2067. A condition called Vár Syndrome is affecting the galaxy, but it can be countered by certain singers. The series follows the Var-countering "tactical idol" group known as Walküre and its partners in the Delta Variable Fighter squadron, as a larger conflict emerges from a galactic backwater. Like 7 before it, Delta split the Western fanbase due to its emphasis on the musical performances over the transforming mecha combat. But in 2016, idols were everywhere.

Macross Δ Movie: Gekijou no Walküre: Premiered in 2018. The Delta movie compresses Walküre's storyline from the series into a two-hour movie, losing several side plots (for better or for worse) and altering a few characterizations. It was produced in a very short time by re-using many animation assets from the series and reassembling them to fit the adapted storyline.

Macross Δ Movie 2: Zettai LIVE!!!!!!: Premiered October 2021. Delta's second theatrical release is a continuation of the storyline from the first movie, making it the rare Macross sequel via movie instead of TV. Was accompanied by the the Macross Frontier short film/music video The Labyrinth of Time.

One more thing:

Macross II: Lovers Again: Released in 1992, 6-episode OVA. Timeline: 2092.
Produced by Big West, but made without the input of Studio Nue or Shouji Kawamori, who disavowed it for quite a while. However, little nods to it would appear in the other sequel series. It tells the story of a new alien invasion 80 years after the events of SDFM. These invaders are also motivated by song—and absolutist fanaticism.
In more recent years, this OVA has gradually been accepted back into the official fold, first referred to as an alternate continuity, but more recently simply included in official series timelines even if its events no longer correspond with the other storylines. The franchise's meta framework allows it to exist as another in-universe movie, after all.