Just started playing jarvan, i see a lot of them go with more damage focused builds in TT doing very well. I'm still rather new to him though, what are some good build orders/skill orders?

Tri Force is good on him. Black Cleaver is pretty good on most champions now too. Wit's End and Hexdrinker are good.

Health stacking has always been good. Sunfire and Warmog's.

In general, Jarvan is a pretty reliable champion and you should be able to build to your situation in most games and it should work out. Sometimes you're building aegis first and then going mostly tanky. Sometimes you rush triforce. Sometimes you build the Brutalizer and get some health items before finishing off a black cleaver mid-late game. It all depends on your situation.

what does his skill order look like? It seems all his skills are solid and give good benefits for ranking up

Typically for skills you'll run R>Q>E>W but his e and q are pretty interchangable per your situation. The team stat boosts of E are nice but so are the armor rend and dmg of his Q.

R>Q>E>W

You can basically build any item that isn't for mages in the game on Jarvan and still be at least okay, seriously his build paths are THAT versatile. Although I typically prefer a bruiser/anti carry build. Getting a decent amount of AD on top of some health and a randuins or something.

I don't take a point in his shield until level 13 because more points into Q or E is more beneficial in most situations imo.

You seriously undervalue the slow in his W, then. I always get one point there at least for the slow (running/chasing).

I usually start Jarvan w/ boots, 400g ad sword (can't remember name) and 2 HP Pots.
First Back I generally get Vamp Scepter and AS Boots.
From there if I'm dominating I get a B.F. Sword if Not my next item would be building up a Frozen Mallet.
Usually I end up with something like:
AS Boots, Frozen Mallet, Black Cleaver, Sanguines Blade, pick up maw of malmortis, finally Randuins if they have a lot of AD or Aegis if it's balanced.

start boots sword two hp pots,
rush brutalizer asap buy first back maybe the red stone too, finish black cleaver, finish boots 2, buy giants belt
build path diverts here depending on what you need:
build giants belt into randuins if you need strait armor
build last whisper if you need armor pen
build triforce if you need damage in general
build sword of the ruined king if you need anti HP
build maw if you need MR
build frozen mallet if you need more CC
build bulwark if you want a more tanky team
end builds look something like this:
merc treads, black cleaver, last whisper, botrk, frozen mallet, bulwark
or
merc treads, black cleaver, last whisper, maw, triforce, randuins

skill r>q>e>w if you are carrying
level shield before the standard if you are tanking everything

armor pen marks, flat armor seals, flat mr gliphs, ad quints
9/21/0 masteries going ad in offense for the armor pen

I think its a matter of opinion.

I don't think it's possible to undervalue a 15% slow by the way, fifteen percent is not a great level 1 slow. Sure it's okay and there are edge cases in which it COULD pick up a kill, but I find the extra damage from E as well as the extra %AS and Armor to be more effective in ganks considering jarvan's gank have huge burst, adding to it only helps.

I've played jarvan a ****load and it's definitely not worth putting a point into shield in lane and I rarely think it's worth putting a point into it in the jungle.

Again it's not that it's terrible, I just think an extra point in Q or E (pending what one maxes first) is more valuable most of the time.

I'm debating on getting Jarvan as well.