Sell phone

You can give it to Apple and get an Apple Store gift card in return without buying a new iPhone from them -- but you would need to use the gift card to buy something eventually in order to get the value from it. See: Apple Trade In - Apple

There are other options to sell it online for cash such as Gazelle: https://www.gazelle.com/

Virgin Mobile is lying to you. You can buy and use your own unlocked phone with their service if you want. They even have that as a choice on their own site:

I have no idea why Apple would tell you it's easier to buy a phone from Virgin Mobile rather than them. That's just straight out nonsense. Buy an unlocked phone from Apple and you'll be able to use it with any carrier you want.

The phone you currently have that came from Virgin Mobile is another matter. Since it came from them, it's locked to their service. Only the carrier can remove such a lock so it can be used with a different cell provider.

Then it's also a matter of how long you've had that phone. Rule number one for any carrier:

There's no such thing as a free phone!

You're paying for the phone in monthly installments as part of your bill. That's why there's a penalty for ending your service with them early. It's mostly so they can bill you for the remainder of the phone's value. And for extra insult to injury, even when the phone has been paid off at the end of the contract time, your monthly bill doesn't go down. They love that.

If you have already reached the end of the contract and you now technically own the phone, they're still under no legal obligation to unlock it. They should, but that doesn't mean they will. If you can (and they won't provide you with an unlock code), try to sell the phone on eBay or other service. You can always get more for it than trade in value. But you do have to make the buyer aware it's a locked phone that will only work with Virgin Mobile's system.