tl;dr: All three quests give you the same 3 starting and it only affects initial form, changeable anytime, doesn't matter.
Mandragora's the best one of the starter 3 to level to unlock stuff that you want later.
Long braindump: You eventually have to level all three to unlock other stuff anyway. Do what vibes.
Theoretically, long-long term the most efficient way to do everything is level 30 capped in Buburimu Peninsula with the good nuking instincts - some combo of:
Scorpion I (10 Earth Affinity)
Rafflesia II (10 Earth Affinity, 5 INT)
Antlion II (10 Earth Affinity, 30 SIRD)
Sandworm III (20 Earth Affinity)
Flan II (10 MAB, 10 FC, 12 Quick Magic because Flan III is bugged and it's secretly on this one instead)
Treant III (10 MAB, 20 SIRD)
Eft II (7 MAB)
Coeurl II (7 MAB)
Black Mage's Instinct (10 INT, 10 MAB, -10% elemental magic spellcast time)
to the max of your points*, then any mon with a BLM variant you oneshot almost anything in Buburimu with Stone II and you level off spam-completing RoE objectives. (if there's no BLM variant, use RDM variant + thunder MAB, if there's no RDM, use DRK + ice mab, if there's no DRK, tough luck you gotta melee stuff but at least you can hit the PDL cap via all the the +atk/str instincts that exist)
So that's a mild argument for beelining Earth Affinity, so of the three starting species the only one you explicitly have to level is Mandragora -> Sabotender -> Flytrap -> Rafflesia.
You then spend Infamy to unlock:
Beetle -> Scorpion -> Antlion
Leech -> Slug -> Sandworm (don't sleep on Pygmy Sandworm which is tiny and hilarious, but you swap to Gigaworm at a cost of 25k Infamy at level 60 to get 30 levels of spell grinding)
Raptor -> Eft
Slime -> Hecteyes -> Flan
Sapling -> Treant
and also
level starting Rabbit -> Tiger -> Coeurl
BLM instinct has no requirements, it's just Infamy (note that these
job-specific Instincts cost 10,000 Infamy normally, but only 5,000 if you've done the Maat or equivalent LB5 fight on that job. I assume you've done them all already, because this is the MR thread, but I'm still saying it explicitly.)
*note that "the max of your points" goes up by a whopping FORTY when you have pvp setting on and 30 cap enabled if you have at least 25,000 Infamy stockpiled, which is why you have to do that all the time to get the power creep to do the low level oneshotting