I think that the best way to begin is by sorting through your items. Figure out what to keep, donate, or throw away. This makes packing much easier and reduces the weight you need to carry. You should focus on packing one room at a time. This helps keep things organized and makes it simpler to unpack later.
To maximize space in boxes, you can use towels and clothes to wrap fragile items. Not only does this save money on packing supplies, but it also reduces wasted space in your boxes. This helps movers know where to place each box, and it makes unpacking more efficient.
Make sure to pack a separate essentials box with items you'll need immediately, such as toiletries and a change of clothes. This way, you won’t have to rummage through all your boxes looking for chargers and toiletries as soon as you arrive.
Remember, if you're hiring NYC moving services, the moving company may offer packing and unpacking services, as this page shows: https://www.jpurbanmoving.com/. That's something to consider if you want to avoid the trouble of doing it yourself.