The second decision is the route your calls take to the provider. Twilio's documentation lists two ways to connect a trunk: over the public internet, or over its private Interconnect service. Either one is an IP connection. They differ in who runs the network in the middle.
Atlantech Online described the same choice from a carrier's side in a July 2016 article. In the first arrangement, which it calls bring your own bandwidth, a business buys internet from one company and phone service from another. Each call leaves on the internet connection and crosses the public internet to reach the phone provider's voice switch. In the second, the office's connection sits on the same network as the voice switch. Atlantech wrote that calls on its network go from the office to its switch without crossing the internet. It also wrote that it tags voice packets for priority, which it can do because it manages the equipment at both ends.
Priority for voice works only on equipment that someone has configured to honor it. Microsoft's guidance for Teams says to set up quality of service on every segment of a managed network. A priority marking set in your office doesn't ensure that the other networks a call crosses will honor it. In the arrangement Atlantech described, the path from the office to the voice switch is under one company's management.
An ordinary internet connection from another company is still a workable choice. Atlantech's article says the bring-your-own arrangement can work well enough for a small company. Whether the provider's connection suits your office depends on the quote, on what the service covers and on what a phone outage would cost you. For a phone system you run, the same decision is covered in what kind of internet connection you need for SIP trunking.