The cost to build a website in New Zealand (NZ) can vary considerably based on your website requirements and who you hire. If you search hard enough, you can find people willing to build a basic site for less than $500. However, most full time professional web designers will charge between at least $1,000 - $10,000. Complex transactional websites will be much more expensive - possibly even in tens of thousands. Generally, you will get most value from working with an experienced self-employed website designer. Web design and digital agencies tend to charge more due to their overheads. Agencies also do tend to include other web and design related services which can add to the cost of the overall site delivery (things like branding, search engine optimisation, pay per click management and social media channels).
How much you should pay for an e-commerce website largely depends on your requirements and how much you are prepared to do yourself. For a custom design built in a system like WordPress, expect to pay at least $5,000. You may also have to cover the cost of additional software so you can hook up the website to your preferred payment processing system.
E-Commerce websites can get quite complex and have a lot going on with product display, lots of data entry, payment processing, security, shipping calculations, coupon redemption, sales and so forth.
So, even just analysing a client's requirements for e-commerce can be time consuming for a website design company.
If you are happy to use a pre-made design and a system like Shopify, and also do some of the work yourself (such as product loading) you may be able to find someone to assist for $2,500. Bare in mind, that if even if using Shopify, if you need extra add ons from Shopify you will have to pay an additional monthly fee to Shopify.
It is generally not cheaper to re-design an existing website. The simple reason for this is that websites age quite quickly, so there's often not a lot left that's very useful to work with. Most web designers will therefore treat a website re-design as a new site build - unless you have decided not to change any of the page names, menu system, or text or images (basically just adding a new 'skin' to the site).
The main difference between a web designer and a web developer is how much skill and experience they have in design and technical areas. A website designer has more of a design focus, they come up with a look for a website. Website designers are also technical and can build and deliver the entire site too (without the need for a programmer). Web developers look after what we call the 'back end' of the website, they are more like software programmers - writing more advanced code when that's needed. Most web developers don't design, they only code (but there's always the exception - and they are often called 'unicorns' as they are not common).
Web designers can build most small and medium sized business websites along with e-commerce sites. You need a web developer if your site needs custom built technology that can't be purchased off the shelf - or if it needs to connect to an API.