With respect to your question about financing, I recommend that you make a downpayment of at least 20% to prevent PMI (private mortgage insurance) from being tacked on as an additional expense. Beyond that how much additional down payment depends on your other investment options as well as well as your available cash flow.
With respect to the "potential" tax deduction associated with rental properties. You will only be able to treat the property as a rental, properly reportable on schedule E on your 1040 return, if you charge your parents a fair market value rent. I would even recommend that you have a standard, written lease commonly used in your area drawn up and adhered to. Further, I would recommend that you establish a separate bank account to receive rental receipts and make payments from for all expenses. Doing so establishes that you are treating the property as an investment rather then as a personal property or second residence.
The issue here is that you are going to have family residing in the property. By having your parents in the property without charging a fair market value rent, the IRS will disallow all deductions associated with the property except for property taxes and mortgage interest. Under Internal Revenue Code Sec. 280A your parents are considered family and their use of the property without paying rent (or paying a below market rent) would be considered "personal use". Their use would be attributable to you, thus, it would be as if you used the home as your second residence.
In order to be able to deduct expenses beyond property taxes and mortgage interest (i.e. H.O.A. fees, insurance, gardening, repairs, depreciation) you need to treat the rental like an investment/business and your parents as if they were not your relatives. Otherwise, you just have a second residence that you treat for tax purposes just like your primary residence.
The only difference between your primary residence and this second residence would be that when you sell it you will not be able to take advantage of the once every two year gain exclusion ($250K if single, $500k if MFJ) available under IRC Sec. 121 for primary residences. Instead any gain would be subject to tax. If you held the property more then one year the maximum tax rate would be 15% capital gains tax (5% to the extent the gain would be subject to the 10% and 15% brackets). If the property is held for one year or less the gain is treated as ordinary income subject to tax at your marginal tax rate (i.e. like wages and interest income).