So on my Jarvin build i go more Dps than tank with him, i see a lot of people tank as him, which he can do but i feel hes way better as a Dps kinda person. with my build i start off with doran's blade, that could be switched between the shield also, whichever you prefer. Then when it comes to boot it always just kinda depends. if theres a person with stuns or snare, any of the sort, i usually get the mercury treads. I the got for madreds razor for a bit of damage and armor, then getting tear of the goddess for some mana, after getting the tear start spamming out your moves to build up your mana pool. i get golden aegis at lvl 4 for this reason, because shortly after getting to lvl 4, if your doing decent you should almost have the tear, allowing you to just use it while walking to get more mana. I then finish up my razor by getting wriggles lantern, i like this item for the life steal, that way i dont have to buy another item later on to make up for it. Then i finish up the manamune. Then i start build up some health. I go with heart of gold first just for the extra gold it gives you. Finishing up that item i get randuins omen. I then move onto the Black cleaver it gives a decent amount of damage and some attack speed. If you can manage to get this far into the build in a game, I would recommend selling your dorans item and getting something else maybe some more damage, maybe a little more health. That parts kinda up too you. Some recommended items i would think about getting would be something like infinity edge, maybe last whisper, or even buy something more along the lines of warmogs or if needed maybe force of nature. Just some possible ideas on another item to buy if you get to that point in the build.

The reason i choose my skills in the way i do is, his flag gives you and nearby allies added attack speed, and at higher lvls can do some decent damage if it hits a champ. also his flag is a good way to scout out a bush if needed. The added attack speed that you get from the flag also helps when taking out turrets, and can help too turn around a battle in your favor. Jarvans ultimate can prove to very useful if timed well with teamates like nunu who have an aoe ultimate, forcing the enemy to stay in that area taking massive damage.

Im not big on jungling but because getting madreds razor is rather easy to get it could give you a bit of a boost early game by jungling. I would recommend if no one else on your team needs it, to get the golem buff as soon as possible. getting this in early game can help out a lot also.

Pros
Hes got a pretty good combo to open up with, also knocking the opponent in the air.
his ability can also come in handy in team fights. allowing you to do some nice damage to whoever you team wants to attack.
He is really good at harrasing in early game and keeping your opponents out of lane.

Cons
Really my only bad thing with this champ is his mana, his moves don't take that much mana to use, but you don't start with much mana either.
When using his ulti it can trap your teammates inside also, so if your going in to help a teammate make sure they're out of the way first.