The thing with teleport is just that it's so good if you wanna go back to lane fast and also late game when u can tp into fights or even tp home to save turrets/nexus. I would say teleport is the way to go with Jayce. You dont need a ignite to kill people.
If u were to go ignite u must have good control in you're lane so you dont get pushed back early and need to b.
Flash is a must. Jayce dont have to much escapes he only got his movement speed when he switches forms. Which is good but the flash is a must and it's very efficent!
Jayce W in both forms arent the best of the best as i use to call it. He get 3 fast AA in he's ranged form and gets like a AoE damage in his Attack form. So dont bother maxing
On the other hand Jayce & in both forms will do so much damage with just a . Since it gives him Armor Pen. He's E - Q combo in ranged will boke everyone down really low in just a second.
His Q in Attack form will jump to the enemy and slow them with sick damage.
His E in Attack form will knock the enemy away from you which is very good as a counter to Riven/Yasuo etc... If ur getting ganked u can knock them away with you're E and then run away to safety. A really good safety spell which will do lots of damage when its maxed out!
Starting items: Both of the starting sets works. i would recommend getting the dorans blade tho. since it gives you 3% life steal! And the pots isnt very needed if ur playing against Non ranged enemies but u might want to consider that if u are up against ranged emenies!
Core: Always start of with buying you're tear so you can start stacking it and having you're muramana not to late about 20-30 minutes depends on how the game goes.
Black clever is a must after you buy you're tear! It gives you Cdr AD and reduces the enemys armor with lots so you're spells will just do so much more damage then before!
Duskblade is what makes Jayce so op with the poke... The armor pen is sick so he can just penetrate through everything even tanks... The stack of a black clever and duskblade will reduce the enemies armor with so much that it dosent matter how much armor the enemy team is building!
Situational: So when you start comming to late game and you got you're core items finished. I usually start of by getting a bloodthirster so i can the life steal and can survive more.
Ghostblade is not really needed im buying it so i can get the extra movement speed on proc and the Lethality if needed! If u dont already have 40% CDR buy the CDR boots. if not you can either buy or
Swiftness boots for the extra movement speed. Merc for more MR which can be good if you're up against lots of AP!