Since you are going bottom you will want a support with you, such as a Sona, that can not only stun her enemies, but can also heal her allies. This will save you health pots, meaning you won't have to go back to fountain often and you can keep accumulating money, to get some higher items, such as a bloodthirster, early in the game. Another ideal for a support is Janna. The reason i think this is not only can she use her 'q' to stop enemies from chasing you if you get in trouble, but she can give you mana, and I have found that Jax relies heavily on mana until the late game. For enemies you will want to lane against, hopefully, a Master Yi. This might seem a bad matchup to some, but with the cc that Sona can do, Master Yi will not be able to get away using his ult, as it doesn't slow, it stuns. A bad person to verse would be a Darius or a Varus; Varus would be a pain to deal with because of his naturally long range and his ability to poke quite easily. And because i have included no armour items, a darius would be bad to deal with because of his ult, which can destroy you if you have around 4-5 bars of health, maybe more depending on their build.

Alot of you might say "Wow, this guy is dumb, he has the worst build idea ever". Don't bag it until you try it. The reason i have 'boots of mobility' is because jax is only supposed to run to the battle, he rarely has to run away from it. This is why boots that have a +movement spead of 5 are perfect. The same goes for the phantom dancers, they not only make it just that easier to get to the enemy and possibly save a team mate, but it also gives you a pretty decent attack speed. You don't have to use two phantom dancers, you can swap one out for a rabadoon's deathcap to have just the edge over your enemies when you use your 'w' and then your 'q'. I prefer the two of them, so that not only are you getting healed by your two bloodthirsters but you are getting healed at an escalated rate. The Infinity Edge is just there to help you take out enemies, whether it might be an enemy champion or a monster, such as baron or dragon.

Sorry if i have set this guide out incorrectly, this is my first time.