There’s really no best or recommended method, you have to create something that fits best into your scenario. Besides safety there’s also aesthetic side of that question, that is, if you care or if it matters.
If it is a clothes closet the ideal way to comply with safety requirements and make this closet “clean” looking would be to frame the vent pipe maintaining at least 1” clearance to the wooden frame (unless you go with metal studs) and drywall it. For a pantry type closet where there is no clothing that could come in contact with the vent pipe you can do nothing, leave it exposed, and just keep any flammable materials at a proper distance.
For the floor and ceiling penetrations (unless that’s been done already) use collars designed specifically for this purpose.