Can TurboTax support married couples filing jointly? Or which products support that? I didn't see anything about this point on the webpage or descriptions of the products

Of course TurboTax can support joint tax returns.  Any version of the software will let you file a joint return with your spouse.  

To begin a new joint return on TurboTax:

You will not be able to merge two previous TT account to start your new joint return.  You can transfer ONE of your 2018 returns into a new return, so choose the most complicated one.  The other spouse’s information needs to be entered manually.

When you enter your own information in My Info, you have to answer the question "Were you married?"  If you click the button for Married, then a drop down will appear that asks, "Do you want to file this return together with your spouse?"  Then you choose yes to file a joint return.  You would then enter your spouse's information into Personal Info.  Whenever you are entering income information there should then be a spot for you and for your spouse's income information.

When you file your tax return you can choose from the possible filing statuses on the Form 1040:

Single, Married Filing Jointly, Married Filing Separately, Head of Household (HOH) , or Qualifying Widow(er) 

The software version you choose does not make a difference as far as what filing status you use.