Within New Zealand:
I use flat rates in my store, based on weight. Everything is sent by NZ Post, at the "overnight" rate.
Overseas:I use DHL as they're fast and secure. Australian customers can order online. Everywhere else in the world, just use the contact page to get in touch or email email@example.com.
Apparel is sent in compostable/ recycled plastic bags.
Prints are sent either flat or rolled, encased firmly in cardboard.
Fragile items (eg ceramics) are sent in cardboard boxes and all cushioning/protective material is either repurposed or biodegradable.
I use the unofficial Courier Rule when parcelling things up: "Will it still be in one piece if it's dropped from a height of 1.5m?"
Any questions, just ask.