Keep in mind that depreciation is a double edge sword. Folks selling crappy rentals often tout the "tax advantages" of their bad rentals, claiming the by taking depreciation and ending up with a passive loss you save on taxes.
On a rental property, both depreciation and interest are deductions against the income. Its not a choice of one or the other. The biggest benefit for depreciation is to reduce the tax bill on the rental income.
If you do have a passive loss (negative net income after all deductions including depreciation) you may be able to use that to offset other income. You can if your passive losses are under $25K and your AGI (as a couple, in your case) is under $100K. If AGI is over $150K, that $25K "special allowance" limit is zero and you cannot use the passive loss against other income. Between $100K and $150K the $25K limit phases out by $1 for every $2 of AGI over $100K.
The other edge of depreciation is that it reduces the basis for your property. That means when you sell the gain is higher. Further, the gain is divided into two parts and has two different tax rates. The amount of gain up to the amount of depreciation (taken or allowed, whichever is greater) is subject to a tax on unrecaptured depreciation, currently your ordinary marginal tax rate, but capped at 25%. The remaining gain is subject to capital gains tax. Assuming you're held for at least a year, that's 15%.
If you live in part of a multi, you will be able to take depreciation on the part of the property that's rented. But not on the part you occupy.
The usual rule of thumb for splitting improvements and land is 80% of the purchase as improvements. A better way is to look at the county assessor data. They usually split up land and improvements. Use their numbers to compute the ratio for your property. Then, as you do certain things, the IRS has different depreciation periods for different things you do. Its a bit more complex that what @Anthony Dooley says, but that's on the right track. Flooring, for example, gets a five year depreciation period. Though if you actually get five years out of carpets in a rental you should count yourself very lucky.
If you go down this road, you will want to find a real estate knowledgable accountant to help with taxes. Taxes will no longer be a DIY project.