For entry-level Macross, try this order:
Macross Zero (no brainer since it's so damn pretty)
Macross Plus (optional, but helpful)
(at least 3-4 eps of the 1982 SDF Macross to get the main invasion story)
Macross Frontier
Macross Frontier was very noob friendly in my opinion. You can get the full story without anything else, but you're missing out a lot of the referential stuff, which is just "lost potential" really, not a fault.
Zero is short, and has quality post-2000s animation, it cost a lot more per episode to make than Frontier so it's a no-brainer. For CGI Macross, it's the best animation, followed by Frontier. There are some character connections right at the start of Frontier that tie into Zero as well, so that can help give more sense of the Macross "world" to the Frontier experience.
The main singer in Frontier is also a homage to Sharon Apple in Macross Plus. And since Plus is short, that might be good to show as well (but after wowing him with the more modern "Zero" special effects).
It's really a shame not to see the original Macross before Frontier though. But even a small number of SDF Macross episodes would make a lot of difference in picking up references in Frontier. One possibility would be to watch the first 3 eps of SDF Macross then watch the movie, DYRL (explain that the story in the movie is slightly different, or he could carry on the TV show). Since the movie lacks the invasion introduction, but packs the rest of the relevant information in. That's probably as compact as you could get it and still make sense.
Macross 7 is a definite no, and there aren't enough Macross 7 references in Frontier to bother, really.