deluxe or premier

It doesn't matter.  You can use Deluxe.  All the Desktop programs have the same forms. You just get more help and guidance in the higher versions.  You only need Premier for capital gains if you are using the Online web version which will be only for 2019. 

For 2016, 2017, and 2018?  You are too late to use online software.  Since you must now use desktop software, use Deluxe.   It will have all of the forms and schedules--all desktop software has all of the same forms, etc.   If you have complicated investment income entries and need more help you can upgrade to Premier if you need to.

To file a return for a prior tax year

If you need to prepare a return for 2016, 2017, or 2018 you can purchase and download desktop software to do it, then print, sign,  and mail the return(s)

https://turbotax.intuit.com/personal-taxes/past-years-products/

Remember to prepare your state return as well—if you live in a state that has a state income tax.

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Note:  The desktop software you need to prepare the prior year return must be installed/downloaded to a full PC or Mac.  It cannot be used on a mobile device.

If you are getting a refund, there is no penalty for filing late.  If you owe tax due, then file and pay the amount due as shown on the Form 1040, but expect a bill later from the IRS for the penalty and interest you will owe.  Only the IRS will calculate this—TurboTax will not calculate it.

NOTE:  Mail each tax year in its own separate envelope.  Do not try to mail them together  or you risk one or more of your returns being overlooked or discarded.