Hello this is my first build. At the beginning i am going to tell you that English ain't my main language and there might be some problems :) And this build is premeditated to 3 vs 3 matches.

If i need to describe rumble it would be tanky mage because of hes good survivablity if you build him right :)

Even amongst yordles, Rumble was always the runt of the litter. As such, he was used to being bullied. In order to survive, he had to be scrappier and more resourceful than his peers. He developed a quick temper and a reputation for getting even, no matter who crossed him. This made him something of a loner, but he didn't mind. He liked to tinker, preferring the company of gadgets, and he could usually be found rummaging through the junkyard. He showed great potential as a mechanic. His teachers recommended him for enrollment at the Yordle Academy of Science and Progress in Piltover, where he may very well have become one of Heimerdinger's esteemed protégés, but Rumble refused to go. He believed that Heimerdinger and his associates were ''sellouts,'' trading superior yordle technology to humans for nothing more than a pat on the head while yordles remained the butt of their jokes. When a group of human graduates from the Yordle Academy sailed to Bandle City to visit the place where their mentor was born and raised, Rumble couldn't resist the temptation to see them face-to-face (so to speak). He only intended to get a good look at the humans, but four hours and several choice words later, he returned home bruised and bloodied with an earful about how he was an embarrassment to ''enlightened'' yordles like Heimerdinger. The next morning he left Bandle City without a word, and wasn't seen again for months. When he returned, he was at the helm of a clanking, mechanized monstrosity. He marched it to the center of town amidst dumbfounded onlookers and there announced that he would join the League of Legends to show the world what yordle-tech was really capable of, without hiding behind a foreign banner.

''Ugh, it's gonna take forever to scrape your face off my suit!'' - Rumble

Okay I prefer Greater marks of insight because they help rumbles damage a lot :)
Both of the seals are good but rumble is pretty weak against hard hitting casters like annie, kassadin, malzahar... so I would take health seals over the armor.
At glyphs i would choose the magic resist ones , but if you like to hit a lot then go for the ability power ones.
All of the Quintessences are good. Just pick what you like :) I am using the health ones.

I prefer the 9-21-0 build.

Okay I always start with the Doran's Shield. After that i move on to mercury treads. After that to rylais. Next one is all about the enemy team if they got a lot of casters go for abyssal if they got a lot of melee dpsers go for cape. If you still feel a lack of survivablity on armor or magic resistance go over the rabadons to hourglass or Force of Nature. And finally take the rabadons for extra ap.
You can also take Force of Nature if you feel lack of magic resist

Flamespitter is your main spell use it when farming and when fighthing with other champs. you should always max this first. Scrap Shield is ur chasing/getaway skill use it when chasing low hp champions or when escaping from a battle. You should use it to block spells too. Electro harpoon your E spell is great spell for extra damage and good CC, but its a skill shot.
Your ultimate is just a perfect. it lands down a rockets witch deal a massive damage , cc and great dot if you stand on it. But the landing is bit hard sometimes. Always use it at team fights or finishing off wounded champion.
Priorities=
1.The Equalizer
2.Flamespitter
3.Electro-Harpoon
4.Scrap Shield

Ghost: Great chasing, escaping ability i use it nearly always.
Flash: Great chasing, escaping ability i use it always.
Heal: Great for fb, i use this sometimes.
Cleanse: Maybe good if u got much CC enemies on your enemy team.
Ignite: If you feel lack of dps, take it.
Smite: No, you aren't a jungler.

Feel free to comment and give me feedback :) And hope you enjoy my build. Pictures and more information coming in future.