If your goal is COR, I'd take this path.
MNK to 18 > WAR 37.
WHM isn't a bad choice to 37, either, but it adds a subjob you'll rarely ever get much use out of after 30 for COR, save for some endgame scenarios, which you're a long ways off from anyway. Take levelling WHM at your leisure and definately finish it as a sub, but I wouldn't use it as a primary subjob.
When you hit WAR 30, unlock the follwing jobs:
Ninja, Ranger, Dancer, Scholar, Blue Mage.
I would polish off NIN as the first sub, since both NIN and WAR supplement RNG very well, you many even like RNG so much you wish to take it further, so these are good subs to have for RNG as well. I also recommend RNG to 40 because it gives you a welcome spot in some money making BCNM fights like "The Worms Turn," which will also help you get the NIN scroll Utusemi: Ni for your NIN sub.
Benefit of each subjob:
- Ranger - Highest possible accuracy with two Accuracy Bonus traits and you can gain on COR and best overall damage potential.
- Dancer - Adds healing, status cure and enfeebling potential through the use of your TP and you can still use melee gear whereas a mage subjob would force MP gear on your Corsair. You can gain one accuracy bonus trait under this subjob, putting it at a close second to Ranger
- Ninja - Helpful with pulling and nullifying damage in various situations. Decent accuracy potential via Dual Wielding +Accuracy daggers, but it doesn't come close to subbing Ranger.
- White Mage - best potential for healing, Status cures, Raise and Reraise can be helpful. However, it forces mage gear on you, which conflicts with CORs ranged accuracy, attack and AGI needs.
- Red Mage - Offers RDM the cures of WHM, Dispel and Magic Attack Bonus, which enhances the damage of your Quick Draws.
- Blue Mage - Offers decent curative ability, protective self-magic and also offers the Magic Attack Bonus Trait. Set Spells allow you to also gain other job traits and stat bonuses.
- Scholar - Offers most of the curative abilities of WHM and DNC via Addendum: White. Dark Arts, Drain and Aspir help with personal HP and MP restoration. Sublimation at 70+ give COR an extra means of getting MP back on top of Aspir and Evoker's Roll.
- Black Mage - Offers highest Magic Attack Bonus Trait under subjob for the biggest boost to Quick Draw, but that's about all it offers. RDM or BLU would often be better for thier curative options.
- Bard - COR is seen as a party buffer, BRD helps enhance this function in some situations, though COR's buffs are often good enough to stand on thier own. March and Ballad buffs are also a fair addtion to COR's list of existing buffs.
- Warrior - Basically an epeen subjob for merit parties at high level. Best possible damage potential, but at the expense of accuracy you could gain from using Ranger, Dancer or Ninja subjobs.
Corsair is a rather versatile job, but generally seen as a party buffer. My personal opinion is that CORs should focus on their damage potential pre-endgame levels and weigh it out evenly with thier buffing responsibilities. Pre-30, the /WHM route is perfectly fine, but the higher you get, it only presents mixed priorities in gear. /WHM is also commonly used in endgame, which I have no issues with. But at EXP levels, its value is marginal at best, better to help bring the damage or cure with a Dancer subjob at 30+ than go with any /mage sub.
Finally, since you'e seen the pretty daunting list I've laid out for COR's subjob options, I'd encourage you to just take all the jobs out there for a spin before you settle on COR. You may find there's another job out there that you like better than what you set out for.
I set out to be a Red Mage and a Dragoon on my original character, I even got Bard all the way to 75, but ended up not being satisfied as any of the jobs. I ended up enjoying Corsair, Ranger, Dancer, Scholar and Beastmaster quite a bit more.
Give all the jobs a spin before settling on one, you may be surprised that you've ended up on a different path than the one you initially set out one. Some jobs can get as involved with subjobs as COR, if not moreso, while others have a more limited spectrum of subjobs they benefit from. Paladin would be a job that really only makes use of three different subjobs - Warrior, Dancer and Ninja. Summoner really only uses White Mage and Scholar, though that's not to say the path of a summoner is any less trying, they have to obtain the Avatars for summoning, after all, and that can be daunting as well.