Is it true what they say about older homes having “good bones”? Should I stick to Houston-area homes less than 10 years old or be more open to older ones?

First-time buyer. Single female in mid-forties looking at 2/2.5 townhouses inside the Loop with a budget of $300k max. I’ve been looking at townhouses built no later than 10 years ago, but these prices have me thinking, would it be terrible to buy something that was built in 1965 or 1977?