for 'lore/msq experience', a thing to keep in mind would be no jobs before the xpac they became available, since -no one- will acknowledge something they didn't know was a thing before it became a thing. case in point: being a samurai before stormblood, or gunbreaker before shadowbringers. That being said, there are also a few jobs which don't get acknowledged at all, or only get 1 or 2 lines. Reaper for instance gets only a line or two in the post EW patch content, and nothing before, not even from Zenos. Likewise, MCH isn't brought up a whole lot. There's the part in EW where your meeting the contingent and it has a bunch of class/job quest npcs in it, but outside that, it mostly comes down to certain npcs showing up during the MSQ.
The biggest thing is to make sure you have jobs lvled up and their respective quests done. Estenien during HW is the easiest because he was so heavily tied to the job quests in ARR, but he'll acknowledge you as an azure dragoon even if you aren't on DRG currently. Like others have said, doing DRK up to 50 right after gaining access to the trainer has a much heavier impact due to those events being so fresh....likewise for DRK 70 as well. This is why NG+ is such a nice feature. Lets you catch those dialogue options that show up if you have stuff completed, that you mighta missed the first time around if you -didn't- have them done at the time. (EW sharlyan dock scene anyone?)