If I have two prior years to file for (2016 and 2017), which program should I purchase? The 2016 version (& re-use for 2017) or buy 2017 ver. (and do 2016 return first)?

Sorry you need to buy each year separately.

If you have a simple return You can fill out the blank forms for free.
Here are some blank forms & instructions for 2017
1040 https://www.irs.gov/pub/irs-prior/f1040--2017.pdf     
Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2017.pdf

1040A https://www.irs.gov/pub/irs-prior/f1040a--2017.pdf    
Instructions https://www.irs.gov/pub/irs-prior/i1040a--2017.pdf

1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2017.pdf    
Instructions https://www.irs.gov/pub/irs-prior/i1040ez--2017.pdf

2017 Tax Tables https://www.irs.gov/pub/irs-prior/i1040tt--2017.pdf
Publication 17 Tax Guide for 2017 https://www.irs.gov/pub/irs-prior/p17--2017.pdf

Don’t forget your state.  And you will have to print and mail your returns.  So be sure to attach copies of your W2s and any 1099s that have withholding on them.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.


2016
You can fill out the blank forms for free.
Here are some blank forms & instructions for 2016
1040 https://www.irs.gov/pub/irs-prior/f1040--2016.pdf     
Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2016.pdf

1040A https://www.irs.gov/pub/irs-prior/f1040a--2016.pdf    
Instructions https://www.irs.gov/pub/irs-prior/i1040a--2016.pdf

1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2016.pdf    
Instructions https://www.irs.gov/pub/irs-prior/i1040ez--2016.pdf

2016 Tax Tables https://www.irs.gov/pub/irs-prior/i1040tt--2016.pdf
Publication 17 Tax Guide for 2016 https://www.irs.gov/pub/irs-prior/p17--2016.pdf

You will have to have both -- the 2016 version to file a 2016 return and the 2017 version of TurboTax to file a 2017 return, as the software is changed for each year to conform with the IRS form changes and tax laws related to that particular year.

See more information on filing a prior year return below:

https://ttlc.intuit.com/replies/3301770

If that's the case, then I don't understand this (appears at the top of this page: <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/personal-taxes/past-years-products/">https://turbotax.intuit.com/personal-taxes/past-years-products/</a>).

I have emphasized confusing part with asterisks.

File past years' taxes for 2017
Select a tax year below and then the right TurboTax product you need to complete and file 2017 taxes ***or other past years’ taxes. If you’ve already purchased a previous year’s CD/Download tax software you can access it here.***

The website makes it sound like I just need to purchase it once.

There are 3 tabs.  You can only buy the last 3 years.  You have to buy each year separately.  Click on the 2016 tab to buy 2016.

2016