i don't know
that depends on your play style
xin zhao got a lot of crowd control (abilities that disables the opponents also known as CC) and he's definately a nice starting champion
jarvan is a new champion and i never played with him but i find him very strong

I highly recommend only buying champions after you have tried them. There's no way we can know who you will like, and you'll be using up a ton of IP that could be spent better. If you have 5-10 champions you enjoy playing unlocked, farming up some IP to buy runes goes a lot more quickly, so buying a champion blindly at a later date isn't as big of a deal.

Xin is free right now and he is a SICK character, Jarvan is good too but Xin has a really fluid and IMO easy playstyle. He is a good character for people that like to be aggressive because he is a stellar, really top of the line initiator and assassin. Jarvan takes a lot more finesse especially with his ultimate.

Jarvan needs to be beef or tank imo. His ultimate is a death sentence for squishies without a flash/blink, and is great for aoe teams. He has a gap closer to initiate (the flag + spear combo, as well as his ultimate), and a defensive spell, making him great at either role. If he goes pure dps, I feel he just puts himself in too many situations where he'll die instantly way too often.

I'm pretty new so I can't give you the "Definitive" guide to Jarvan, but I made a few friends the past couple days and one of them plays Jarvan and one plays Fiddlesticks.

The Jarvan would open the arena, the Fiddlesticks would crowstorm and then jump in, and basically ANYONE on the wrong end of that died. (They nuked a nunu from like 80% with that combo). I imagine an Annie or really anyone with hard ranged DPS could really mess up someones day once they get arena'd as well, and probably a lot of other heroes of all sorts that I'm not experienced enough to know about.

Jarvan requires teamwork though so for newbie PUGs I'm not really sure how I feel about him. That's why I like Xin, because he doesn't really need any support and he can just make it happen on his own and his AOE ultimate is useful in team fights without any coordination whatsoever.

Standard + Lance isn't for chasing, it's for initiating. You need someone like Yi or another fast character that can move around quickly to chase and "Clean up" after you lane into them and burn them to within sight of the pearly gates.