Hello Mango and Welcome to the Forum:
I recommend using the fiberglass tape on the sheetrock joints. You just stick it on and trowel the compound over it. It may be a little rough the first time but a spray bottle of water will soften it enough to gently scrape the ridges off. Trowel it once again, using more finess this time. A light sanding should finish it up. As for the peg board, I would use a piece of wood trim such as casing on that joint because you can't keep it from cracking with the joint compound. The ceiling is just another corner with the walls; handle it the same way. There is a neat trowel made for corners; I highly recommend it.
Glenn
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