Pretty Basic early game champ, clear, gank if you can. Jungle path is rather normal as well, make sure to keep up on vision control, and get some ganks off at least. You need the runeglaive, insane clear, Stalker's for the slows is also really handy.

Really important by now to have the 30% cdr, the luden's will give you a boost in movespeed to catch up to the enemy. Rabadan's is like, an heavy ap carry. Hextech is due to jax giving in some good mixed damage. The order depends on what you need. If you need to keep clearing jungle, hextech is better. If you want damage, luden's is probably the first pick there. Pick good fights, picks are probably best around this time. Get dragon quickly, and you should be fine. Don't try excessive team fights if you aren't ahead, or not by that much.

You can have a heavy impact split-pushing because Jax. But team fights are always open. You are still really good at making picks, but team fighting is almost always jump onto the back line, get them down in 2 w's usually, q-w, stun, w. You can escape pretty well due to the 30%-40% cdr on the q.