I had a cheap one from Tesco in my last house and it worked perfectly. Mind you, it was before the complete digital changeover had taken place and I was using it with three boosters in the circuit.
When I moved into my present house I changed to Freesat and gave the Freeview box away.
Certainly, for a small TV in the kitchen, I would go with the cheapest box you can find. After all I suspect your good lady would not be interested in HD, Surround sound or even 3D whilst frying the odd breakfast egg or two!!