Must I move in first and live for some months before I can rent it out?

I assume this occurred in California, so the Ellis Act would apply. I also do not know whether this is a single family house and whether your family was going to pay any kind of rent. But you do not state which city and each one can have different laws as to must proceed. Violation of any one of the numerous provision can result in your not being able to get out of the rental business and hefty fines. You need to speak to a local attorney who handles such matters on the landlord side; normally an initial interview is free so that the attorney can tell you if they can help [find out exactly what they are going to do, how long it will take to do those acts, and the expected cost to you]. First of all, you should have tried to re-rent once the tenant left and your family decided not to move in. Your ability to claim loss of rent damages from the prior tenant would end after a "reasonable" period of time to try to re-rent the property. Secondly, I have not read any cases on the Ellis Act but I assume a good faith effort to move your family in [supported by a good reason why they did not as otherwise a judge will assume they never did I do not understand what they had to worry about the prior tenant so that they did not move in, unless it was that they did not know how long it would take to evict and they could not wait the unknown period of time] and not the actual moving in is sufficient. Thirdly, we need a lot more information to determine if the tenant has what appears might be a valid claim against you. If you followed all the local and State provisions and notice provisions, the tenant would have no right to stop paying rent and could be evicted with the giving of a three day notice and a successful unlawful detainer suit [if you did not do that correctly, you might have to start it all over again or have no right to evict]. Did you already go to court, does the tenant have a good job or money to pay a judgment against them, are your parents willing to testify, is the former tenant represented by an attorney [some tenant attorneys are almost impossible to deal with as they view all landlords as the spawn of the Devil], etc. Good luck.

Based on the information you have provided, there appears to be no reason why you cannot rent the property to a third-party at this time.

First of all, you should never give a reason to terminate a tenancy. You just do it. You can rent the place.