I do really well starting with shield for rumble if I'm going against ADs with good early game. If it's AP or I plan on ganks/kills early, I get boots/pots. My first item is usually revolver, so I shoot for 1200 by getting a kill or farming enough before my first back (if I get shield first I will buy boots first, so enough for boots, a tome, ward. pots then). I used to go straight to WotA but with the cost nerf, I am getting the giant's belt first after revolver. From there I usually build a cap if I'm ahead or a scepter if it's double AP. My early boots are usually tabi or mercs and late game I'll sell for sorcs. I finish rylai's as my 3rd AP item as the javelins are enough for early ganks.
I haven't played him since the patch, so I don't know if I'd go kage's into DFG, but maybe that could be a viable item now.
More or less, once I get revolver/giants or Wota, you can't bully me anymore. I will push to tower/farm golems/counter jungle until it's time to team fight.
Rumble is my fav atm as he's very fun to play and powerful. So far, Corki is my bain.