>>1058172>are they all chronological/related?Yes but not strictly so, they're stories in the same universe that do somewhat follow on from others at times with some references to characters but they're not direct sequels with the same cast or anything.
Pic related is the order of the franchise, the only thing it's missing is Delta and the Delta films (only the first is out currently) which as you can probably guess come after Frontier.
If you say you're not really a fan of "that old art style" then I won't say start with the original series because that series is a bit rough at times visually even if you do like the style, I would perhaps reccomend starting with Do You Remember Love however; it's a film version of the events of the original series (not a re-cap film, I think it might be entirely original animation) and the original series does kind of set the backdrop to the entire franchise so I'd say watch that and see how it goes, if you aren't enjoying yourself drop it because you won't miss out on anything major (and that goes for all entries really).
After that it depends where your preferences for art style lie, II is non-canon and entirely irrelivant to every series that comes after but would otherwise come directly after DYRL going by when it came out, Zero is a prequel to the original series, and everything else is in both production and chronological order. You don't need to watch both versions of Macross Plus, hell I still haven't seen the film version, but I've heard the difference is the OVA has more fights and the film has a better finale. And also much like DYRL, the Frontier Films are not sequels but instead a different version of the events of the TV series so even if you dislike Frontier give them a look bcause I've seen people that love the films and hate the series (oh and also there are three versions of episode 1 of Frontier but google will explain that one to you when the time comes).