an Armourer I have experienced first hand the need to have quite a few "Subs" and after talking to other people in game it appears that Armourer is the most need heavy class when it comes to these.
As such I'll try to put out there the needs/advice on subs for the Armourer class in FFXIV.
As any subjective issue what I might consider most important is not necessarilly the same as other people but I'll try to put the most important first (IMO).
Leatherworking 35+
This is mainly because it will be needed in quite a few recepies as a second skill, top example being Iron Gauntlets that needs LW35.
Also, Fulfillment, an ability available at rank 10 will be very useful as it improves rate of success on all crafting actions.
Having LW up to speed will also allow you to repair (mainly) your belt and boots.
Important to me is also that both ARM and LW share Cobbling Training, Glovemaking Training and Hatting Training which will allow you to save some of your ARM Guild Marks for ARM specific training.
Since a lot of the recepies in LW use the same shards as ARM once you do leves for LW there is a good chance your receive those all so important shards to grind on ARM.
LW will also enable you to make some of the mats you require for more complex ARM recepies.
Weaver 25+
Also needed in quite a few ARM recepies, these at the moment only go up to WVR25 as in Iron Cuirass.
Maybe more importantly is the ability to repair your gear, quite a lot of it and at 18-20 you should be able to repair Canvas gear almost everytime.
Maybe not as important as Fulffillment, Masterpiece is still nice to have, specially if you doing leves of 3-5 ranks below your own.
WVR will also enable you to make some of the mats you require for more complex ARM recepies.
Just like LW, WVR also shares Glovemaking Training and Hatting Training, once more enabling you to save Guild Marks.
Alchemy 10+
At rank 10+ you should be able to turn Crystals into Shards 95-99% of the time, to me this is the most important help from Alchemy as eventually you will get Crystals as leve rewards and not have enough shards to grind with. Once you get to 14, 15 it should be much safer to do them without the need for facilities.
Preserve is considered by many as the best godsent ability of all and I accept that is very usefull, specially if you atempting recepies 5+ ranks above your own.
Goldsmithing 35+
Amongst others, Goldsmithing is also needed to craft items like Iron Cuirass.
As with Blacksmithing, Goldsmithing can be useful in smelting ore into usable crafts for Armourer, this will only really be benefitial if you also have Miner to provide the Ores.
At rank 10 you get Epiphany, not very useful but if you don't have Masterpiece you can then use this ability to try and increase quality on crafts.
Blacksmithing 30+
The most usefull things to come from doing BS are the abilities Maker's Muse atainable at rank 10, Ingenuity and Sublimation, both obtainable at rank 30. Sublimation specially will be very handy when you try to get those HQs with your ARM's off hand tool.
The usefulness of BS will only really come into effect at 20+ when you will be able to craft Iron Nuggets out of the ore, untill then you might also get the leve rewards which you can then turn into usable mats to grind ARM with.
BS also shares Smeltting Training with ARM and as such is another chance to save some ARM Guild Marks.
Miner 25+
Maybe unexpectadly, Miner is not that usefull to ARM unless you also dedicate yourself to do Blacksmithing and/or Goldsmmithing since ores will require BS or GS to be crafted into nuggets. It's need will become more apparent when you start needing Iron to grind and belive me, you will need quite a lot of it.
Prospect is a nice extra bonus as it will save you time running around to deliver those all important leves, personally I by passed Prospect III in favor of Prospect IV at rank 26 for only a difference of 4K Guild Marks.
Carpenter 30+
Investing in Carpentry will only really benefit you if you intend to make shields as some of them require it as a sub skill.
As a bonus you will receive Tender Touch at rank 10 which will reduce the ammount of durability you lose on both successful and failure attempts (personally can garantee it can reduce up to 3 pts per synth attempt).
At the moment, at least I cant really remember anything else you might need to consider when thinking about starting ARM but if anyone has any ideas or questions feel free to put them forth!