Dude. Stop with the color coding. Seriously.
I just spent 5 seconds trying to double click the first piece of blue text thinking you can compiled a spread sheet of "wtf" gear for PUP, then I noticed the random colors across your post and stopped reading...
Meanwhile, you're a bit late to the game on this one. It was way way worst before the cap was raised above 75. The first decent set of melee gear that pup really appeared on aside from random pieces was either part of "end" game (Enkidu/Usukane) or was stuff like Cobra/Pahluwan. Mirke was the first non-AF/Relic piece that was greatly specialized towards the job's needs and that was only because of the augments.
Looking back and remembering to ignore the synthesis stuff, you can still say how painful it was to be a PUP back in the day.
Post 80, though, PUP's options open up quite a bit now and with Verethragna (even without it), you find yourself being able to contend with just about all DD's. Additionally, the automaton is capable of some potent and exceptional damage all its own, not to mention being able to tank quite effectively in some scenarios. PUP's not really in so bad of a position with regards to gear anymore.
Not to say it isn't still one of the least loved jobs, but its way better than it was when I was slaving to build PT's for it and having people drop out haphazardly saying "lolPUP".
EDIT:
And PUP being on mage gear was not a mistake. The original intention for the job was for you to match via subjob what your automaton was going to do. You go to a PT with Mage puppet, you sub a mage job, Healer? /WHM. etc. etc. The game's community just never endorsed the idea [read: it never worked as well as SE imagined it would because of the Automaton's wonky AI] so it never took off, and SE, for fear of making PUP too powerful, never gave them the tools they needed to make it a reasonable expectation that this style of play should work. PUP started to find a more efficient and practical home as a damage dealer and solo'er -- when SE came around to the realization that their original plan didn't work, they started giving us better DD gear.
PUP is on mage gear because it was supposed to be uniquely capable of emulating other classes, but the plan never came together. Additionally, if you do the research, you'll find that your burden rates are affected by the differences between your stats and your automatons -- If your automaton has more INT than you do, you generate more burden per Ice Maneuver and so on for each other stat with DEX having some undisclosed affect across the board. (which is why the advanced animators give DEX boosts.)
I know its kind of the trend of the game culture now with how quickly you can level a job to max -- but you can't really jump onto older jobs, especially ones with histories as sorted as PUP or say, DRG, and just start talking about them without doing any real research into how things have worked out thus far... A lot more goes into it than "Puppetmaster is a melee job."
No, Puppetmaster -became- a Melee job. Where it is now is, despite how well it works and how enjoyable it became, quite a bit separated from what SE originally intended. The same thing is likely to happen to Geomancer and Rune Fencer, as it happened to Corsair, Monk, Ninja, and even Beastmaster.
Could probably toss Dragoon, Summoner, and Red Mage on that list as well.
EDIT 2:
Side note, some of the most successful PUP solo'ers I knew pre-75+ were PUP/Mages, and utilized a full set of mage gear for things such as Mount Zhaylom burns and the like.