When shipping the iPhone in for repair, should I leave the SIM card in it?

I would say take the SIM out. Should they not be able to repair your phone and send you a replacement, it would be best to have your original SIM. That way all you need to do with the new one would be to pop out the SIM it comes with and put in yours. Then when you have to do the reactivating thing, you wont get charged for it. You'll go through an abbreviated activation. Also if your getting a temp phone, you'll want your SIM to use in that one too. If you've opted not to get the temp phone, then you can always put the SIM into another ATT phone if you have one. You wont get the visual voicemail, but at least you'll get the calls you might otherwise miss.

Is Apple sending you a loaner iPhone to use during this time?

If so, you need to remove your SIM card in order to use it with the loaner iPhone but you should do so regardless. Apple may decide to exchange your iPhone instead of repairing it and the exchange will be shipped without a SIM card.

You should also erase all data and settings on your iPhone before being shipped to Apple for repair or possible exchange.

On the iPhone, go to Settings > General > Reset.

Select Erase All Content and Settings.

If you call back and ask nicely, you may be able to get the fee waived for the loaner iPhone. It is policy to charge for it but not a hard fast rule. The worst they can say is no.

You're welcome.

The iPhone only which there is room for only.

If your iPhone is exchanged, you will be sent an iPhone only - not the entire retail package which isn't necessary.