I'd recommend you look at getting the deal with the Service Provider, as the possibility of having security misconfigurations on your own WordPress instance is far higher.
Going with a service provider restricts the amount of things one can configure (or misconfigure!)
Feel free to reach out to me if you need more input on this topic :)

My vote is for Wordpress. Webstarts.com looks pretty janky. Also, as Rohit notes, you can really limit yourself with a full-service provider like that.

Wordpress has come a long way in the last few years and rivals Shopify in some respects (marketplaces, for example) for a fraction of the cost. Also, the developer ecosystem is incredibly robust. You can find pretty affordable and competent remote devs on Upwork; but it pays to do your own research as product manager and know which plugins, theme, etc. you want to utilize. You can find cheap hosting with the likes of GoDaddy or Bluehost, or go premium with WP Engine (recommended). Hope that helps.

That totally depends on what kind of website you want to build, your budget for building the website and if you'll be building them yourself and whether they need to scale in future and add more complex functionality.

The platform must be chosen for the functionality and build approach and for your budget.