This is my first guide so sorry if it is not as detailed like some of the others (like the threats section... sorry not sure all the threats to Ziggs and some of the ones I have seen as threats to Ziggs which I have played against don't seem like much of a threat).

Sorcery and Inspiration (possibly the best set up for just about all casters unless Support)

Arcane Comet for obvious reasons (or should be obvious reasons) should be your keystone on Ziggs.

Manaflow Band for some sustainability in lane so you can stay in lane as long as possible before 1st back to get Lost Chapter and Boots (hopefully together).

Transcendence for the CDR (obviously CDR is great for tower pushing since your W is up more often which means bye bye tower if you are there and it is low enough), also good for harassing enemy champions with your abilities, since Ziggs should be (in my opinion) the last one of your team when disengaging from the enemy team (such as leaving their base after taking a turret and inhib). If you don't want the CDR then go with Celerity for the MS which is also good for being last one out of enemy base if they show up to defend.

Scorch for early lane harass. This essentially gives one of your abilities an lesser Ignite effect every 20 seconds when used on enemy champion. If you don't want the early lane harass then obviously go with Gathering Storm for the extra AP over the course of the game.

Inspiration runes
Biscuit Delivery every 3 minutes (up to the 12 minute mark) you get a "cookie" that restores and permanently increases your max mana. Great for staying in lane longer to farm.

Cosmic Insight for CDR... who doesn't love CDR especially when it also applies to your Summoner Spells and Item cool downs.

Start building Morellonomicon as soon as you have enough for 1st back (1200 is the best but 900 will do). Lost Chapter for the +300 Mana and +25 AP. This is better then the other branch as first since it also gives you better lane sustain combined with Manaflow Band and Biscuit Delivery runes. Your 2nd item should be Lich Bane for the MS and the extra damage it gives your AA. Next build Liandry's Torment for the health, Magic Pen and the burn effect it causes. Having the extra health is good for being the last line of defense for your team. Follow that with Luden's Echo for even for MS and even more harass from its proc. Finish with Void Staff for the Passive of ignoring the enemies MR (if they have built any, if not then go with Zhonya's/Rylai's/Rod of Ages as best of the items you could get for final item)

Start with Q for the long distance poke/harassment of your enemy laner. Next go with E since does damage to multiple minions and great for harass if you toss it right under enemy champ. Then finally start your W good for harassing enemies and getting away from ganking enemy jungler if used properly. I have looked at other guides and they are having you Max out W last.... they don't even say to put 2nd point into W until your other 2 abilities are maxed out. This is ridiculous seeing how the whole point of Ziggs is to BLOW UP ENEMY TOWERS when he is able to with his W. I personally prefer maxing out Q last, alternating points into W and E (W being primary) and obviously putting points into Ult at lvls 6, 11, 16. Ziggs is also not just the guy (sorry Yordle) that makes towers disappear if he is there he is one of the best champs for getting your team mates out of enemy range with his W and E.

Ziggs is the Yordle that makes towers go bye bye. There is really no other way to describe him. Not everyone really understands the destruction this champ can cause I think since there have been plenty of times I get no help from my jungler in pushing lane as much as possible. Since Ziggs W can instantly take the remaining HP from a Tower if it gets to a certain percentage (depends on what rank: higher rank means faster you can finish off the tower) you want his lane pushed and pushed hard so he can take the tower as soon as it is possible for him (I'm not saying camp his lane and don't go get your jungle camps or gank the other lanes but if you are near him go help him seriously). This then can free him up to start roaming much easier and help push the other two lanes and get towers faster to put enemy team at huge disadvantage with how fast they lose towers. Ziggs is also good for being the last line of defense for your team if you are in enemy base and they recall or re-spawn from death and are forcing you out, Ziggs with proper build can easily keep away from the enemy champs all the while using his abilities to harass the enemies making them back off.