My experience is that whenever you feel you are doing not enough damage, you are actually surviving but unsatisfied with killing mobs too slow. The fact is, there is no "too slow" as long as you survive, especially as a monk.
Try to focus on items with physical resistance if you really want to build tanky, while keeping your resistance up. Your weapon should have fast attackspeed to keep spiritgenerating up so you have more options for dealing damage/healing.
The monk is half a caster half a melee character in my opinion so you shouldn't attempt to kill them with just your spirit generators. Try actually spending your resources as soon as they are aviable and your damage will automatically increase.
Also try a good mix of Dex/Vit on items. Resistance against impairing effects is good, as is damage against melee attackers. But both shouldnt be your main focus.
I also tried a full on damaging monk with max dex, life on hit effects and lots of evasion but i found that vitality and armor through shields was missing.
In patch 1.05 the drop rates were doubled and Monster Power added a new bonus.
Using the base numbers from the Blizzard forums:
Max Max
Non-inf Inferno
base MF 100% 200 300 400 475 500 600 625%
normal 0.0036% 0.0072 0.0108 0.0144 0.0180 0.0207 0.0216 0.0252 0.0261%
elite 0.0440% 0.0880 0.1320 0.1760 0.2200 0.2530 0.2640 0.3080 0.3190%
It is now trivial to get 100 MF with paragon levels and NV stacks, so I usually assume the 100MF line as the new baseline. With the 300% cap in place, bonuses from NV and bonuses from MP the new max MF is 475% in Normal, Nightmare and Hell (produced experimentally by hitting the cap in Act 1 Normal Monster Power 10). The shrine does not bump this to 500%. I am uncertain if the upper limit is 625% or 650%, as I cannot get 5 NV stacks in Monster Power 10, Inferno, but if it behaves like Normal then the max is 625%, calculated as max. 300% from equipment + paragon levels + 250% from MP 10 in Inferno + 75% from 5 NV stacks.
Empirically, running between 325 and 375 I've been seeing a legendary or set item about every 4 or 5 hours of game play, using Act 3, Monster Power 3. Most of them stink, but that's another discussion all together. I've also had sessions where I've popped 3 in a matter of an hour at MF 260% MP 3 Inferno. I also see a legendary about every full act run at max MF in Normal (sometimes none but usually 1 maybe 2).
Keep in mind that each monster kill is an independent event. The odds are not cumulative, so killing 50,000 white mobs at 475% MF does not guarantee you a legendary pop (though I'd be somewhat startled if you didn't get one). You still only have a small chance on each individual kill to see a legendary or set pop. People often misinterpret the probability of independent events to think that doing more of the same will increase their odds. The odds on each kills stays the same. What changes is the odds against seeing another consecutive failure. See this question and answer for a mathematical treatment.
So let's look at the odds of seeing a legendary or set pop after repeated mob kills.
So what is this graph saying? Looking at the 100% MF for normal mobs line, it says that after about 3,000 white mob kills there is a roughly 20% chance that you will have seen a legendary pop. On the Elite 625% MF line it says that there is roughly an 80% chance that you will have seen a legendary pop after 500 elite kills. It is very important to note that none of these values ever equal 100%, even at 32000 kills the number is still "very close" to 100% but not quite.
Tracking these curves it is very clear that even for large numbers of kills the probability of seeing a legendary pop can be very low for normal mobs regardless of MF, but that it is much better to hunt elites for even less than 1,000 elite kills at any MF. It is for this reason that most serious legendary farmers are getting their 5 NV stacks and killing as many elite packs as they can find, not lingering about with white hordes.
So does this match up with the assertion that you kill 10-30 times the whites is as good as killing elites? Looking at the 60% probability line, at 100% MF against elites, if you are killing 10 times then that's better than the 100% MF against white mobs, it's acutally on par with 300% MF against whites. If you are killing 30 times then the 100% MF normal line is actually above the elite line. My battle net account shows that overall, including levelling at all difficulties I am averaging about 20 whites : 1 elite, just as an arbitrary number for consideration. As a level 60 I target elites, so I suspect this ratio is decreasing but it will take some time for all the levelling to be averaged out.
The maximum pop chance from a white mob at maximum MF is still about half of the base chance for an elite. This fits with my empirical experience. I have popped legendaries off white mobs but far more off concentrated attacks on elite packs.
One thing that changes the scenario somewhat, that I've failed to make note of in this answer is that an elite kill gives multiple pops many (not all) of which have a chance of being legendary. Normal kills only give 1 or 2 chances. As both NV and MP add extra items into kills. If we assume that an elite gives twice as many items as a normal (an easy assumption) then with my white:elite ratio we should only use the 10x comparison, and then clearly the elite killing strategy is modestly better. If we make assumptions about 5 NV stacks or higher MP levels then this gap widens.
It is very clear there are diminishing returns for adding MF. The distance between the lines shows there is a large gain for going from 100 to 300 MF, a smaller but decent gain between 300 and 475 MF but a very minuscule gain for pushing to 625%.
If there are hidden mechanics working behind the scenes or if the base rate is incorrect, then this picture will evolve with time.
Best Answer
As for what items to augment first, it doesn't really matter, but in general you should augment items with better rolls. You are already using icy veins guides, so on this page Gear reccomentadion you can see desired rolls for all your items. If you have ancient items with good rolls - go for it, it doesn't matter if it's weapon or some other slot.
As for gem level, for season journey it's required to do augmentation of at least 50 level gem. Each gem level will give you 5 points of primary stat, so if you sacrifice level 100 gem you will receive bonus of 500 primary stat. The gem itself doesn't matter, you can use any legendary gem. Attribute is chosen by Flawless Royal gems which are required for recipe as well. For Monks, I think, dexterity is preferable stat, so use Flawless Royal Emeralds.
As for multiple augmentation, you can augment item more than once, but only the latest augmentation will be effective. High level augmentation makes sense only if you are going to push higher greater rifts.