Like a trip to the grocery store, many things go into the cost of a custom website, so the final number for a simple, custom site largely depends on your "shopping list". Do you need branding? Copy? Photography? The starting range will be from $2,000 - $4,000 depending on what goes on the list.
The price goes up from there if we add additional technology such as SQL database, custom Ecommerce carts, streaming video, etc.
The reasons you might own a website instead of renting one are similar to the reasons you might own your residence rather than renting. First and foremost, it's yours. If you want to make improvements to it, say, add a pool or repaint it, you can.
Likewise, if you want to customize your site, you will have to work within the limitations of WIX because you don't control the toolkits and fonts that the servers support.
Furthermore, you will have to pay WIX in perpetuity, which is a sunk cost if you later decide that owning your site is the right move.