I built a shed out of leftover materials that the builder abandoned. Metal siding, roof material, J-channel. I had to buy some corners but it was cheap, about $12 for 10 feet if I remember correctly. Built out of 2x4 framing, on a 5' x 5' home-poured slab (sack crete, reinforced with some left over steel angle), and the framing is all screwed to the crete. My little shop is only 30x40 and I don't do a lot in the shop BUT from previous experiences with the compressor being inside the shop, I knew I did NOT want it inside, not at all. If I have the radio on, I want to be able to hear it. If the GF comes out to the shop, I want to be able to hold a conversation. And that I can do all that with the compressor in it's own outdoor shed. The shed is kind of built onto the shop building. The shed foundation has about a 2" gap between it and the shop concrete foundation, this also reduces the noise and vibration. I have vents, one at the lower part on the East side of the shed and another on the upper West side, so that air flows right through. I don't use my compressor for painting or anything that would require a lot of compressor run time...usually an impact wrench, maybe die grinder once in a while, etc.
Now at work (lawn mower shop), the compressor is on the other side of an interior wall. When it comes on (often), you hear and feel it. If I'm standing there talking to a customer, we have to go outside if the compressor is on. This is a 100 gal compressor, so it's not a small or quiet one. I thought maybe the boss would invest in a screw compressor but I would imagine that he will someday, I figure AFTER the cows fly home.