Back to the original question.
BPF says the quality of the instruction is prime and I'd second that.
During your PPL, the aircraft type is not really important, relatively, IMHO.
It's a shame you don't have a C152 available, as they tend to be a little less expensive and are also a good learning platform.
Whatever people say about Cherokee handling, they are safe. Very safe. Very, very, very ......
Given that stability and agility tend to be at the opposite ends of a continuum, perhaps it is not so surprising that the handling is less than razor sharp, but neither will they do anything nasty, unless seriously abused, so it makes your workload a little lighter and builds your confidence on pre-PPL x-countries, if you choose the PA28.
On the other hand, if the Tecmnam operator has better instruction, I'd go there.