Here is how the tax will work on your LLC. Your LLC needs to file its own tax return, on Form 1065. It will taxed as a partnership. You and your girlfriend will each receive a Schedule K-1 from the LLC, which is how the income passes to your individual return. The TurboTax program for individual tax returns will not help you with this process.
To complete the partnership return, you first need to calculate your basis in the property. This is your purchase price, plus all of your other expenses (closing costs, interest, utilities and renovation expenses, including labor) incurred up to the day you put it into service as a rental. The "phantom" expense you referred to is called depreciation, and it is calculated from your basis. You depreciate the value of residential rental property (minus the value of the land, which doesn't get depreciated) over 27.5 years, but your depreciation will be a bit complicated to calculate, because you put your rental into service in the middle of a year. The IRS puts out a publication (I think it's Publication 527) that explains how to calculate your depreciation. Your depreciation will be deducted from your rental income. You can also deduct your property tax, insurance, maintenance, interest and other expenses incurred after you put the property into service. After you determine the LLC's income, you will assign half of it to each member and send them a K-1. This is passive income from a rental, so you will not have to pay FICA on it.
Hopefully Steven Hamilton will drop by and correct anything I've gotten wrong here.