I assume that you are going to try and keep this assembled, so I'll give suggestions with this in mind;
Get some Turtle Wax chrome polish and apply it on all of the areas that you see corrosion and carbon on the manifold and on the carb with a rag.
After you have all of it coated with a film of it, use the rag to wipe the smooth areas that are not cast to get all of the contamination off. You can go over it as many times as you'd like if you continue seeing results. Let the polish sit on the surface for at least a minute before scrubbing it with the rag you used to apply it on with.
For the cast aluminum areas, get yourself some stainless steel wire brushes. I like using the deep wire ones, because they get down into areas that the shorter, toothbrush sized ones don't, but you may want to get one of the small stainless ones for some areas. Like a good BBQ grille brush with long bristles works well. The brass ones work ok, but they can leave a trace of brass on the metal and don't last as long. The ones with the stainless wires work best on aluminum and get rid of dull finish on cast aluminum, even if it's clean.
Scrub the cast aluminum in a circular motion with the wire brush and it won't leave patterns on it. I do this on cast aluminum that I restore out of a blasting cabinet and it completely gets rid of the dull finish. After everything has been scrubbed, tape off the air horn on the top of the carb and hit it with a garden hose and your thumb if you don't have access to a pressure washer.
You can continue the process and catch up areas that need more attention after rinsing it the first time. After you're happy with it, untape the top of the carb and fire it up to get the water off of the engine.
That chrome polish gets rid of cooked on oil and grease residue on my antique waffle iron that is polished stainless without scratching it. It also removes trace amounts of rust and it's pretty cheap.
