I start
+
x3 nearly every game. If you're in base when minions spawn you can wait 10g and buy a fourth potion and run to lane without missing a minion. You can still scout before minions spawn if you recall by 1:20
I play Fizz mostly defensively levels 1 and 2. I start W for easier last hitting and maybe to counterattack an enemy melee champion. I don't look to push the lane as Fizz very early because you can't push very fast early and I want easy access to the last hits... so if the lane gets frozen too close to his tower it sucks for a few reasons... Often I grab E level 2 in case I need it for a defensive purpose or I need to damage the minions or splash a little extra dmg on the enemy champion.
The reason I am not aggressive with Fizz until 3 is because auto attacks on the enemy champion cause their minions to attack you. Fizz Q also does this because it applies your auto attack damage (normally champion abilities do not draw minion aggro). Once we're level 3 we have our full kit and pretty sick trading power, by this point you should still be full hp with all your potions.
The most optimal way to trade on Fizz is to W + Q into them, auto them a few times, then you can use your jump to all in or retreat. When you jump with E you lose minion aggro instantly. Engaging with Q rather than E also means you have an easier out if you were baited and the jungle was there... Of course in reality we are probably using E to dodge the enemies CC spell or primary damage spell in the trade...
Super long range champions can probably stay away from your Q range though. Maybe in this situation you might need to close the gap with E, but this kind of move is much riskier. I've been playing a lot of Fizz lately and I've never had a problem closing the distance with Q tho... Maybe because rather than going for a crazy dive move I will start roaming if my opponent is that passive.
I actually favor investing extra points into W before maxing E. The reason being is it's more damage potential when going all in, it's more mana efficient damage and it allows me more freedom to use E for the utility rather than be forced to use it for damage early game. Against enemy ranged champions that can instantly peel you off them though you might not be able to get enough auto attacks to make W worth it, however I guess that's what using E to dodge is for. So typically I have 3 points in W at level 5 but still max E by level 10 (only 1 level later than normal).
After six I strongly prefer it to save my ultimate for point blank range. If you throw the fish from far away you give them a real chance to dodge and you telegraph that you're going aggressive. When going for a kill with ult close the gap with one of your other skills and ult at close range. The potential ranged catch potential of the ult is a lot more useful later in the game though when you are grouped with your team.
As for the build now... I will typically grab 1 dorans ring and continue into either abyssal sceptar if vs. AP, or versus AD I will go sheen into zhonyas. I'm not really fond of the sheen, as lichbane is not a good rush item. Sheen is nice when you can first afford it though, but it doesn't scale well until you finish lichbane.
I think CDR is very valuable on Fizz, so I've started building the lucidity CDR boots instead of sorc's. They're even cheaper too. Having high CDR on Fizz greatly increases your chances of surviving fights, especially with Zhonyas. If I'm behind tho I do not prioritize the CDR (never happens with I play Fizz lately!), it's more important you are able to do enough dmg to the enemy squishies...