You're "allowed" to choose on whatever basis you prefer. My former T was older (I was in the age range of his kids) and it suited my need for a paternal figure, as well as for a T who was well-trained, well-credentialed, and with a solid reputation.

I'm in a different stage of my life now, and my concerns aren't mental illness, or even psychological, really. More philosophical issues of life stage, so I absolutely wanted an older T, and preferably a woman. While she has the training to spot anything that might relate to psychological processes, we don't work within a psych paradigm. So her age and life experience is crucially important. As well as her willingness to be open to learning about the experiences I bring to her.