Do I need a design first?
For a whole section, usually yes, and some landscapers do design and build together while others price from a plan you already have. Say which you want, because it changes who is the right person to ask.
When is the best time to plant?
Autumn and early spring for most of New Zealand, so roots establish before summer. Hard landscaping such as paving and decking can be done year round, weather permitting.
Can it be done in stages?
Often, and it is how most people afford a big section. Ask for the work broken into stages with prices, so you can do the structure now and the planting later without paying twice for access.
Who moves the spoil?
Ask, because it is a common gap between quotes. Excavation produces more material than people expect and disposal is a real cost, so it should be stated rather than assumed.