I am not a great tournament caliber player, and I dabble with ranked. I will say that right now. I don't have fancy ranked scores or anything, but I did make a build which if I can complete is for the most part unstoppable...

PROS:

-Very good early game
-Can kill tanks and squishies at about the same rate
-Good CC
-High Tenacity
-Hard to kill (Resistances, health, health regen, LS)
Deal huge MAGIC and PHYSICAL damage
-Really good farmer/Tower pusher
-Can work alone


CONS:
-Can only damage one enemy at a time
-Mana*****
-Nothing else really...

Best Summoner spell for a melee in my opinion hands down. Escape option and offensive 1v1 equalizer.
Jarvan IV is a mana*****. Chatting "oom" is the worst thing I can ever say as a carry at full health while backing. In early levels, you can be running out of mana after 3-4 combos. GET CLARITY.

Movement speed is HUGE in the TT, so getting this boost really helps.
This is an AS build because of all the on-hit effects.
I go with straight armor because TT can have short rounds, with early kills, and many quick surrenders. You are more tanky for getting First Blood too.
Same reason as the seals. Just for MR.

This is not a gameplay guide. But I have a few notes for Jarvan IV's skills:

Great Innate. Adds to the Magic Damage you will cause down the road and its huge for early game.
Doesn't do much damage, but its armor reduction is crazy and makes his combo with Demacian Standard badass.
I actually forgot to put this into the guide the first time around. Pretty weak, decent shield for when your getting ********ed. Can slow people your trying to chase. That's about it...
Great Passive! The bonus armor and AS makes the build happen. You can ignore buying a lot of armor because of this. This combo allows you to go through walls which rapes for ganks on TT. Being able to knock up the whole enemy team (lol, ik) with combo can/will change the odds of a teamfight. The active has crazy range for getting a kill and the aura is really nice too. MOST IMPORTANT ABILITY YOU HAVE!
Decent ult. Does a lot of dmg, but most people either have Flash or a flash ability. Good for trapping people in range of turret or keeping them from running away. Can also deal lots of damage when enemies are grouped.

EARLY GAME:
I start with Doran's Shield and Demacian Standard, giving me an Armor of 56 and MR of 51 after runes and masteries at level one! I then get Mercury's Treads to buff my magic resist ( I don't worry about my armor because of the Demacian Standard buff) and to get the best TENACITY in the game. I then get Madred's Razors for even more armor, dmg, and the farming boost.

So far, you should have only spent 2675 gold so far and you already are getting tanky! This ENTIRE build only costs 15815 gold, by the way.

MID-END GAME:
This is where you need to decide which items are most important, you will be buying 3 items with Recurve Bows. I suggest you buy the bonus items( emblem of valour, Null-Magic Mantle, and Madred's Razors) first because the bows can be expensive...

This is the order I normally get them in:

I finish this bow item first because it is the cheapest, it gives you +50 MR while attacking, you get to start doing SOME magic dmg, and the speed bonus allows for you to get your Madred's Razors to proc more for farming/jungling.
Bloodrazor... even more attack speed, +25 armor(all jarvan needs), more physical dmg, AND the 4% MAGIC DAMAGE that makes you a tank killer and gives you a lot more magic dmg. With this and Wit's End you now deal 42 dmg +4% of the target's max health in MAGIC DAMAGE! So much for being a physical carry... Don't forget about opening with Martial Cadence either.
Now to add to the physical part of being a carry and keeping your health bar full. You get 6 health regen per second, 20% Lifesteal which will be your main healer, 40% more attack speed, AND just by standing near your enemies you reduce their armor by 20! Add that to your 26% armor reduction for Dragon Strike and your enemies will almost be naked! Oh and did I mention that your allies get to share in the health regen, LS, and AS fun? Cuz they do.


LATE GAME:
I'm surprised they haven't surrendered yet? You should be 12/1/3 right about now, better than I would be doing... time to make sure this game ends though. You have 4 slots taken up right now because you sold your Doran's Shield right? The next item is actually a must-buy, but it is not necessarily part of what I consider the core of the build, Frozen Mallet

Frozen mallet gives you even more attack dmg, and allows you to have more health for that high resistances of yours. It also does one huge thing, it makes the enemies slowed when they take your onslaught of destruction... they better have Flash, Exhaust, or some damn good CC.

6th item:
This is up to you. But mainly up to your allies and opponents. I have a couple suggestions that I would go with depending on the match.

Best option by far. More dmg and AS. But, you get 45 armor reduction. With Zeke's Harbinger and Dragon Strike enemies now have their ARMOR REDUCED 65+26%. DAYUMMMMMM! Not even Malphite can survive that... +10 armor reduction too if you Exhaust the target and have Cripple(the mastery, for some reason the link isn't showing).
Gives you some crazy AD and LS to add to your Zeke's Harbinger making you deal more damage and heal more.
Even more resistance and even if you die, so what.
Expensive, but nice if you want it.
Crits, AS, and movement speed. Whats not to like?
Physical DPS's gone wild? Damn Tryndamere's...
HEALTH. You are a minion killing machine at this point, stacking this even late game should be piece of cake...
Pansy casters... all I can say is DEMACIA!!!
Jaxkiller. But the high AS boost and more magic dmg is nice. Better to buy EARLY GAME.
REMEMBER TO BUY ELIXIRS WHEN YOU FINISH YOUR BUILD! Some people don't. I do not understand.

With this build this is what will happen just off the first basic attack:
You deal 8% of their current health as magic damage capping at 400.
You deal 42 magic damage and raise your MR 5.
You deal 4% of their max health as magic damage.
You reduce their armor by 15.
You slow the enemy's movement speed by 40%.
Their armor is reduced by 20. You lifesteal 20% of the damage dealt.

YOU DEAL YOUR PHYSICAL DAMAGE!!!

Which should be around 216 before armor reduction.