Should I use Turbotax Deluxe or Premier? I own a home, and have investment accounts

I have the same situation  Deluxe version worked fine for me.

Based on your question it appears that TurboTax Deluxe will allow you to prepare your tax returns.

I don't know that you can effectively file with Deluxe. Premier includes additional sections for handling investments. If you're like me, you may have a lot of closed positions with losses and gains throughout the year. The Premier software has been super handy by importing all of the stuff you'll need for your Schedule D, among other things.

The Deluxe version allows you to itemize and report most investment income.

If you have capital transactions, that is gains or losses from selling stocks, bonds, ETFs, or real estate, you will need Premier. You would also need Premier if you have royalties or rentals. 

Click here to see the forms included with each version.