Jax top is simple. Stay relatively safe early, if there's a chance and you are confident, GET THAT KILL. But for the most part meta champions beat Jax early, so stay safe, get XP, and farm. When you hit level 6 you gain a lot of dueling power off of your 3rd hit minion combo (hit minions twice, then jump on laner for the 3rd hit pop). Jax will scale hard, as long as you get consistent farm and don't feed. Splitpushing is great for Jax, but so is team fighting. Play what your team needs.

Don't invade unless ahead. Jax's early game jungle is just as weak as it is top. He isn't Master Yi, so you shouldn't sit there farming till 6, but don't gank constantly. Manage your time well between farming and ganking so Jax can help his team and scale into the carry he needs to be.