"Self employed" is the name for the Turbotax Online program that handles self-employed workers.
"Home & Business" is the name for the Turbotax Desktop program (installed on your own computer from a CD or download) that handles self-employment. (Yes, brand confusion. Oh well.)
I never recommend the online version unless the taxpayer qualifies for free filing. My reasoning is copied in my canned answer below.
The cheapest way to use Turbotax is to buy the CD or download for Turbotax Deluxe from a discount retailer like Staples, Costco or Amazon, and install it on your computer. If you buy the Deluxe Federal + State + Efile edition, you can prepare as many returns as you want. You can e-file up to 5 (IRS limit) and then print and mail the rest. One free state is included. State e-filing is $25 extra for each state return, but if you prefer cost over speed, you can print and mail your state return for free. The desktop version also gives you full access to all forms and worksheets, including those that are hidden in the online version.
Deluxe (on the desktop only, not online) includes all the forms needed for investments and self-employment. The Premier and Home & Business versions have more help and advice, but if you know what you are doing, you can use Deluxe at lower cost. The only potential downside is that your tax file is not stored in Turbotax's cloud. This means that it is not hackable (good) but also means that you have the only copies. If your computer crashes and you don't have a backup, your file is gone.
Turbotax online has two features that may be useful to some customers: you can work on your tax return from any internet-connected computer as well as smartphones and tablets, and your file is backed up securely online. (However, you will lose access to your old tax files unless you keep using turbotax online--think of it like a subscription.)
Turbotax online is overpriced (in my opinion) and an inferior product. There is only one seller so they control the price. I only recommend online to people who qualify to file for free.
Also, If your total income is less than $33,000, you can file using the TaxFreedom edition, which includes self-employment and other forms not normally included in the "regular" free version of Turbotax. The IRS requires TaxFreedom to be a separate web site, and if you want to use it you will have to make a new account and start over from scratch. https://turbotax.intuit.com/taxfreedom/
Either one will work for you as clergy. Both will allow the housing allowance and W2 as well as self employment income. The TurboTax Home & Business CD/Download version will allow you to do more than one tax return and includes a state return if that makes a difference to you.