Good morning Chris!
Yes, I do believe your approach should match what your goals are. You are looking for something to give to your kids over time. I do believe that either method you mentioned could work. With Turnkey, they are typically move-in ready and take a lot of the stressful rehab out of it. But I also feel that you can pay top dollar for them and they don't leave a lot of equity for you so it makes you rely on the cash-flow which you would still need to do your due diligence and verify. You can't really buy a turnkey property at discount so that takes the "buy right" mentality out.
I can only talk about Colorado Springs and how our market will work for a fixer-upper. We are seeing homes sit on the market for an extra two weeks, sometimes longer than a month now. At our office, we are seeing several homes drop anywhere from $10-30k to close. I say this because its not that buyers aren't out there, but they are absolutely hesitant with rising interest rates and I want you to consider your exit strategies if your fixer-upper is sitting on the market longer than you anticipated.
I would recommend a buy-n-hold property. Work with an agent to find a property that is undervalued, buy it at a discount, now you already have equity built into it. Rent it long term and you can either sell it in 15 or so years to pay for a college or two, use the cash flow to do the same, or continue to hold onto it! Let me know if this helps!