Please correct me if I'm wrong, I'm no expert, I just read a lot.
Ross, as far as your annual property taxes, you are playing the entire amount for the assessed value, which includes the land, and the building.
What you deduct is what the IRS sees as a "loss", kind of. The idea is that a property "lasts" for 27.5 years(residential, commercial is different), and the IRS allows you to deduct the value of the additions(so not including land) over that lifespan of the property.
In reality, we all know that property doesn't expire in 27.5 years, but that's another topic entirely.
What Jason means about the difference between the deduction and credit is a common confusion. The deduction comes from your gross income. As an example, if you made $15,000(and were married filing jointly), you would be in the 10% tax bracket. If you had absolutely no deductions, you would pay $1,500 in taxes. If you were able to deduct $1,000, it comes off the top. So instead of being taxed on $15,000, your taxed on your adjusted gross income, which is now $14,000. So you pay $100(10% of the deduction, relevant to your tax bracket) less, and pay $1,400.
A credit works on the other end. If you had a $1,000 credit, you would take it from the final amount. So if you had to pay $1,500 in taxes, you subtract the tax credit, and you would pay $500.