Monk subs best to a...Follow

You should note that at the maximum level of 70 (currently), your maximum sub-job level will be 35.

Thus, as you sub Monk, your benefits will be seen most significantly at main job levels 10 (Boost), 20 (Counter), 30 (Evade & HPup), 50 (Focus & Martial Arts II), & 70 (HPup II & Chakra).

Now, looking at these bonuses (and factoring in your primarily melee-focused stat bonuses as well), you can see that you want something that can use the ability to make a very powerful initial strike (Boost), and avoid damage (Evade, Counter), while dishing it out (Focus, Martial Arts).

Since Martial Arts is Hand-to-Hand specific, you probably want a job that can use them at least halfway decently if you go that route, or that can ignore the lost benefit. Looking around at some of the items available, Dark Knight may just be your cup of tea. Many of the Claws (HtH Weapons) are available only to THF/DRK/NIN, and have good damage ratios and bonus effects. The DRK can use all of the subjob bonuses to help it in its role (dish out as much damage as you can, or as hate allows), including the active Evade ability and the HPup to increase your survivability.

Other possibilities abound, of course, and in conclusion, I can only recommend that you play what you wish to, and would have fun with. Too many people consider subjobs game make-or-breakers, when that is often not quite the case.