For Online you will need to use Premium to enter a K-1. You can do both federal and state. State is a separate charge. Online is only good for 1 return per account. But you can use the same email address for 5 accounts. You need to pay for each account.
For the Desktop download you can use any version. All the Desktop programs have the same forms. You just get more help and guidance in the higher versions. With Desktop you get 1 free state program download and then it is $25 to efile each state return or you can print and mail state for free. You can do unlimited returns and efile 5 federal for free.
Desktop has several advantages over the Online version.
You can do more than 1 return. You can see and enter into the actual forms. It has a What-If worksheet. And you can use a lower version because all the Desktop versions have ALL the same forms. You just get more help in the higher versions. In online you have to upgrade to enter certain kinds of income. Like Premium for investments.
And the Desktop program is always available even after the year ends. Which is good if you ever need to amend your return after online website is closed or get audited and need your tax records.
You can buy the Desktop CD/Download program here,
https://turbotax.intuit.com/personal-taxes/cd-download/