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Macross has been around in one form or another since the early 80's. Starting with Super Dimentional Fortress Macross 1982, followed by the Movie Macross, Do you Remember Love?, then Macross Flashback 2012, Macross II, Macross Plus, Macross 7 (and it's sequels), Macross Zero, and the latest to date, Macross Frontier.
For me the perfect place to start would be the order it was released:
Super Dimentional Fortress Macross (SDFM), is a 36 episode series with a tidy story that would require no further viewing should you just want to see one TV series of Macross. It has all the elements of it's father series Gundam, but adds a more complex love triangle, and adds Songs! Music become part of the fabric of the show.
Macross, Do You Remember Love? Is a movie length retell of the series with completly redone and upgraded animtation. It however is rather odd to watch if you had not already seen the first show. Be careful of a dreadful Dub that came out in the late 80's under the name Clash of the Bionoids. It's dub could be in the hall of shame for one of the worst. DYRL as of this time has no official dub.
Macross Flashback 2012 is nothing more than a video collage of snipits from the show, and songs sang by the seiyuu of the pop star protagonist. Think "early" version of an AMV. There is no real need to see this unless your already a fan. BUT it does have about 6-7 minutes of new footage drawn at the end, that shows a nice recap/ending of the three main starts of SDFM.
Macross II Is a complete reworking of Macross (it does seem to follow the Do You Remember Love? movie however) It is not part of the main timeline. Being that it is a Macross story in it's own timeline You could watch it stand alone, possibly after DYRL. Also, it carries the Macross badge well enough, by having all the elements. Pop star singing, action, love triangle and intergalactic war.
Macross Plus Is a continuation of the storyline of SDFM. It is set many years later after the events of SDFM. Although it is a continuation of the timeline, it is very capible of standing as a series by itself. It does have, all the Macross elements but it is a reverse love triangle this time, with the aforementioned action and singing. No intergalactic war however, but it is a very short OAV, and also was compiled and shortened into a movie compilation (with slightly different end) So it can be seen in one sitting.
Macross 7 Is the first sequel, that actually follows some of the characters (older) and has cameos and fan-siteings from the first series. It also had the most similarity to the original series at the time it came out. Macross 7 once again, does not absolutely require to have seen the original series, but it would help. There are flashbacks and some references that might slip by if the first season had not been seen.
Macross 7 also has a movie, The Galaxy Is Calling Me, and two OAV series Encore and Dynamite. All of these are good for following side stories, and one is helpful in further knowledge of what protoculture is, but they are more or less for fans of 7 and could be missed if you happen to want to move on. They do not necissarly stand alone very well and would help to have a viewing of at least the 7 series.
Macross Zero A more unique storyline in the Macross continuity. It is a prequel and in the timeline, it falls before the events of SDFM. It is the first Macross that uses computer aided animation (before all were cel hand painted) and it is why I feel it should be seen later. It can stand on it's own as a show, but has a lot more depth if you already have at least seen the first series. One of major characters in SDFM, is a younger pilot in this series. It is not the usual Space war drama, but does have some of the elements of the Macross badge.
Macross Forntier. Is the latest Macross in the franchise, in both production, and where it fits in the over all timeline. It is almost a retelling of the original series in many ways. Love triangle check, pop idol check, intergalactic war check, and is chalk full of references to the other series. From Songs, to machines, to clones of old nemesis' to roll around vending machines, it is all here. However being that it caters to the original fan base, it does not hold up well as a stand alone series. In fact it might be questionable to watch without prior knowledge of SDFM, 7 and Zero or one might not like it much.
There is also two movies for Frontier. One is out, as of this blog and one is due out soon. The first is a retell, and the next will be a continuation of that, but with some changes in storyline. This would be nice to see, due to Frontier's somewhat hanging end.
Side Note; For some the Macross franchise was introduced to us via a cartoon created mixing up the animation from three seperate animated shows from Japan. Robotech, used most of Macross' 36 episodes to make up the first act of that show. I highly recommend seeing where it all started if your a fan of Robotech.