DoH leveling order

Hey guys! Just got to LTW 50 last night, took me around 300k gil in non farmable mats and some effort but it was easy overall. (Stacked 100 leves and farmed all my leather)

My question is, if i want to lvl all the other DoH, which ones should i be leveling first to spend less money on the MW? Ive heard CUL 37 and ALC 15 are a must, but if someone could make a recommendation it would be great.

I've noticed carpenter and weaver-made materials are rather expensive in my server, while alchemist and blacksmith items are cheap, so i guess i would start leveling botanist and then straight into carpenter+weaver but i dont know lol.

Culinarian to 37 is a really good idea, Hasty Touch and Steady hands 2 allow you to HQ items much more easily than without those, because you can save most of your CP for mends and you can get many more touches in.

Alchemist 15 is great too, and I'd even recommend going to 50, getting alchemist to 50 is extremely easy, the leves are very simple (usually 15 potions, you make 3 a shot so it's only 5 crafts for a whole triple turn-in) and it's overall worth it, Alchemists make reagents for many other DoH so it's great being able to do that stuff yourself, and you'll be able to make some more money on the side making SCH/SMN/WHM relics and melding materias into those.

Blacksmith 15 should be gotten ASAP, Ingenuity is an essential skill to make 2star items.

Weaver 15 is also a good one, obviously Weaver 50 is much better but it's much harder to get too (or more expensive if you buy the Diremite Webs and the Fleece).