She will be selling it to me for $120k but is gifting all equity above $85k (my loan amount) which is acting as my down payment.

Conventional loan with an equity gift of 20% to avoid PMI.How did you add value to the deal?

@Joseph Larrew- a  hard money loan for the  down payment likely wont be acceptable ...check with the lender you are using for the 30 yr fixed loan   2)  fyi   gifted  funds  are normally not allowed  for   inv property  purchases   3)  if the  down payment funds are  borrowed  - the main lender  will normally   require that the  down payment loan is  secured by some other asset  ( another property /  car / assets )  and  also  they will factor a  payment into the qualifying ratios    4) maybe a 401K loan ?   

A family member wants to gift/sell a rental property to their child that they have owned for a long time.

They are great multiplicator of wealth when incorporated in your investment cash flow and also provide substantial death benefit for your family if you die early.If your estate will be substantial (over $12M for current estate tax exemption), and if you want to put some money aside for your kids now, you can also look at creating an irrevocable trust for each of them and funding them every year up to the gift tax exemption ($16k yearly currently).

For me, I'm thinking "OK, I'm gonna gift wrap a deal for this kid, is he going to be able to pull the trigger?"  

shell property in inner city may be gifted to me.

There could be some implications with "gifts" or things like that since it's your father, but thats a question for a CPA.You wont need an appraisal since those are typically only required by a bank when you get a loan.The value of the house is whatever you are willing to pay and he is willing to accept. 

@Jennifer WalneThere may be a gift tax return filing obligation.

We thought about the physician loan but the closing cost would be higher than the FHA and we would not be able to use gifts from families and seller rebates.