In my opinion, the garment that most immediately and dramatically upgrades one’s look is a sport coat, or blazer. Slip one on and you look more put together, more elegant and generally people see you as just a bit classier looking than the other guys in just their shirt sleeves. And that is even if you are wearing just a tee under it, though I would generally avoid that choice unless you can really pull it off. Don Johnson not withstanding, unless you are blessed with incredible Italianesque sartorial charisma, a collared shirt is a must under a coat for most men.
One of my dearest friends since my college days comes to our country house for a weekend, packing more than I take for a two-week trip to Europe. His pipes accompany him, in a purpose-built attaché case that holds a dozen of his favorites. I frequently travel on business and carry a spare suit, a few shirts, and other amenities of a man’s life, with two pipes nestled in my briefcase and one in my jacket pocket. Who is right, and who is wrong? That, ultimately, is for the reader to decide, as each approach is a reflection of personal tastes and perception.