iPad Trade-in

I have the original box for my current iPad Mini so does Apple want the charger and USB-Lightning cable in addition to the iPad itself?

You can if you want to, include the cables and charger. It will increase the value. however it is not required you do so.

Do they send a return box or do I have to take the old iPad into an Apple Store?

You can do it either way. If you do the trade-in online, Apple will send a box to ship the iPad back to them. Or you can choose to take into a store and do the trade-in directly during purchase of the new iPad. Its up to you.

See here for more details about the process: Trade in with Apple GiveBack - Apple

If you trade it at the Apple Store, they won't need or want the original Apple Box. They also didn't ask for the cables or charging brick when I traded two iPad's in not long ago. If you do the trade via send back, they'll send you a box to ship it back to them.

From the Frequently Asked Questions section in the Giveback site:

How does it work?

Just answer a few questions either in an Apple Store or online regarding the brand, model, and condition of your device. We’ll provide either an estimated trade-in value or a simple way to recycle it.

If you accept the trade-in estimate in the store, we’ll give you instant credit toward a purchase. If you accept it online, we’ll send you a trade-in kit (at no cost to you) so you can send us your device.

Once we receive your trade-in device, a team inspects it and verifies its condition. If everything checks out, we’ll either refund the purchase method you used to buy a new Apple device or we’ll send you an Apple Store Gift Card via email.

If you choose to recycle your device, we’ll either handle it in the store, or we’ll provide a prepaid shipping label so you can send your device to our accredited recycling partner.

Should I choose a trade-in refund or an Apple Store Gift Card?

It depends on where and when you make a purchase.

If you’re ready to buy a new product at an Apple Store, you can bring your old device with you. If it’s eligible for trade-in, we’ll apply an instant credit at the time of purchase. The only exception is that we don’t currently accept Mac trade-ins in the Apple Store.

If you’re ready to buy a new Apple product online (apple.com or the Apple Store app), you can add a trade-in and get a refund back on your new purchase, once we receive and verify its condition.

If you’re not ready to make a purchase, you can trade in your old device online for an Apple Store Gift Card via email that you can apply to any future Apple purchase.

And no matter how you use Apple GiveBack, if your device has no trade-in value, you can always recycle it responsibly for free.

How long does the online trade-in process take?

Generally it takes 2–3 weeks. But the sooner you send us your device, the sooner we can verify its condition and process your trade-in refund or gift card.

Recycling a device is much faster. As soon as we email you a prepaid shipping label, just send your device to our recycling partner.

This link has all the info you're looking for:

Apple GiveBack

Under Select your device to get a trade-in estimate for an Apple Store Gift Card, tap Tablet.

or scroll down to the FAQ section

I did say this on my previous reply:

or scroll down to the FAQ section

I'm curious, how much is the estimated value based on your input? Which Mini model do you have?