You
could do /drg to 37. You may struggle with invites as many will look at the job combo and get a headache thinking about it, but it's perfectly workable.
If you just want WAR to 37, don't feel that you absolutely NEED to level up MNK especially for that (as Ellipses seems to be suggesting).
MNK's best overall, yes. But not mandatory. WAR/DRG with a G.Axe between 20 and 37 is a potent DD.
As for enjoyment.. Well WAR can be tough when you're missing a lot. Loooooooooong delay on your Great Axe, followed by a
swish! as your weapon meets nothing but empty air. Your innate accuracy will naturally get better as you climb through the dunes, by Qufim you'll still be missing but not as regularly. That helps. Really though, WAR is about nice solid numbers and helping out your tank. Carry a boomerang around too, in case your party needs a puller.
Really, there's no tips on 'how to enjoy WAR more'. You may find it's just not your kettle of chips, but even so, you need it to 37 as you're well aware..
(If you want to go silly, levelling THF up to 18 (THF15 should be on your to-do list anyway^^) and then going WAR/THF at 30-37 can be hilarious with Sneak Attack + Sturmwinds. Sure, you'll piss off your mages, embarass your tanks, probably cause downtime when you die from pulling so much hate... but it can still be a heck of a lot of fun if you have a laissez-faire kinda party.
)
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Food...
Meat jerky/mithkabobs (pure attack/STR) are great if accuracy isn't an issue. Cheap too typically.
Jack-O'-Lanterns are nice accuracy food (+10 to acc and eva). 3 hour food, bring a handful just in case.
Rice Dumplings add a bit of everything, +attack, +STR, +5 acc, other stuff too besides. Great food. Pricey though!
I'd carry meat jerky and a few jack-o-lanterns during the dunes/qufim and use accordingly. From 25 onwards, I personally would switch to Dumplings if my gil was able to support it, otherwise Meat Mithkabob/Jack-O still...