I don't know. I do see what you mean, but I like the way Guinsoo's stacks with his ult, its an absolute must for me. I'm not very aggressive until I get scepter usually, it sounds like you're more aggressive early game.
As for runes, it really depends on the player, I always used to be stuck having people getting away from me because I couldn't attack quick enough, hence attack speed runes. I like the attack damage runes to give an early game advantage if stuck in bad situation.
I just like the attack speed boost, by the end of the game I can get my attack speed over 2.5, which is pretty insane. I don't know... its a preference I guess
I like the idea of lichbane, I will have to try it. As for Trinity force, I had tried it, but I liked having the slow from Frozen mallet rather than other stats from Trinity.
Atma's is something I'll have to try as well.
Thx for the advice :D, keep it coming :D

Meh, not sure if I like this...
I always start with tank runes (dodge/mres/hp) and an Amplifying Tome, getting boots and a Hextech Revolver on the first/second way back.
Jax isn't a great laner, because if you don't get him any tanky stuff or some kind of lifesteal, you'll be zoned out easily. Therefore I prefer building him with burst damage early game, getting a Hextech Gunblade and a second Bilgewater Cutlass for the great slows and the 500 extra magic dmg from both actives. These items will also provide you with insane damage, lifesteal AND health because of Jax' passive.
Also, I found that getting any kinds of attack speed on Jax is a waste, since any attack speed item adds only a tiny bit of AS, compared to his ulti. I'd rather get more AP ( Rabadon's Deathcap), AD ( Atma's Impaler) or survivability ( Guardian Angel).
A second gunblade is never bad, because it will give you even more insane lifesteal/spell vamp. However, I'd rather reserve this for the last item slot.

I can also recommend trying a Lich Bane or a Trinity Force as late game items, they work great with Jax.

I just like to play Jax this way, because it makes his early/mid game great, because of the huge amount of kills you can get by nuking people and regaining your health in seconds.