The NYC Registry Edit: Change.

You need a safe, stable changing surface before anything else; This can be a dedicated changing table or a dresser with a changing tray as long as it has a strap/harness and meets CPSC safety standards. 

No. Most parents choose one or the other, since a dresser with a changing tray converts into a dresser once diapering ends, while a dedicated table is changing-specific. 

Beyond the surface itself, you need a strap compatible pad, within-reach diaper / wipes / cream storage, a disposal system, and a small-space setup if you don't have a dedicated nursery room.

Both are equally safe when the surface has a proper strap/harness and meets CPSC standards. The difference is longevity and footprint, not safety. Read more differences in Dresser with Changing Tray vs. Changing Table.

A dresser-topper combo or portable caddy and pad setup lets you create a changing station in any room without committing permanent floor space. 

The pad is contoured foam or plastic base that provides the safety strap anchor, while the cover is the removable, washable fabric layer on top. You typically need 2 to 3 covers per pad.

A dedicated diaper pail is recommended for odor control and safety since regular trash cans don't seal and can be accessible to curious toddlers.

So long as the pad meets the CPSC's requirements, which pad is better is a matter of preference. Whereas the traditional pads can look super cute thanks to printed covers, they do require regular washing. The wipeable changing pads (like the ever-popular Keekaroo Peanut) are extremely convenient, as there's no laundry required. 

Although you can do that, so long as the tray is built for it and secure, however, we think that the potential hazards (blow outs over your baby's mattress) may outweigh the convenience. 

Now that you have your diaper changing set up figured out, you'll need to figure out your sleep area and a feeding area. Check out our Sleep Checklist for the essentials, as well as tips to manage a smaller apartment.