The first thing I would do is put on paper for your benefit what the mission is. Are you seeking a pilot career, or just want to fly for recreational purposes? How many people will you be carrying on a regular basis? How far away are the destinations? (Like from where you live to where your wife wants to go... New York City to the Cape Cod area, in my case) and what kind of plane will carry the load you intend on carrying (kid stuff like strollers, playpens, and other...). When all that is done, it will come close to defining the plane that is best for your needs.
Now the big question: Is that the plane you want to train in? Is insurance affordable for a zero time student? Can you find a CFI to instruct in that plane? After you slam it on the ground for say 100 crash-and-go landings as you come up the learning curve, is that the plane you want to carry your family in? How difficult is it to find a flight instructor for that airplane? If yes, do it.
Second big question, as mentioned above, how many hours per year do you anticipate flying? It is pretty easy to calculate the annual flying bill if you are a renter. Ownership will most likely be MORE expensive than that, because all of the fixed expenses are paid by you and not diversified among other renters. If you have a bad annual inspection, as but one example: the renter can just walk away and find another plane/flight school. The owner must pony up the repair costs or he is left with an unairworthy aircraft worth a fraction of the value in a sale. One way or another you will pay for the repairs to get the plane back in annual.
So renting during training may be cheaper and with less downside risk. It will also allow you to clarify in your own mind what you want out of this flying thing, without the burden of ownership. Owning brings the absolute freedom and joy of owning your own plane ... as well as the financial obligations of ownership.
Again, as noted above, most people use 100 hours of flying annually as the breakpoint between renting being better, and owning being better - but this will differ with each individual and each plane. I wish you luck with the decision, and also with your training. Come on up, the air is smooth and cool up here!