Both the Tiger Moth and the Cessna 150/152 have trained literally tens of thousands of
ab initio pilots, so you can't go too far wrong with either type.
One advantage of learning on a cessna or piper is that if you go to hire a plane while on holidays, you will be much more likely to be able to hire something that you will be very fimiliar with. Therefore your checkout time will be shorter, and you'll feel more comfortable flying it.
This is true enough, but personally, I would not worry much about this. If you can fly a DH82, you will find it an extremely process to convert to nosewheel airplanes like Cessnas or Pipers: probably an hour of circuits, no more. The reverse is not true, as it will take the average nosewheel pilot 5-10 hours to learn to safely taxi and fly a tailwheel airplane.
Why not intersperse the PPL instruction with the more interesting types?
This is not a terrible suggestion, but for most people it is not a very good one. I think that most students would have a difficult enough time coming to terms with learning how to fly one airplane type, without jumping back and forth.
The purist in me says you should go solo in a glider first!
Amen to that.