Agree with FD that the school, and the instructor, is far more important than the aircraft.
That aside, have a go at both, and see which you like the most. They are so similar in every way that counts that it's impossible to recommend one over the other. I've flown both. I'd say the advantage of the C172 is that it has doors on both sides which makes getting in and out easier, compared to the PA28 which only has a door on the passenger side. The C172 also has windows which can be opened during flight, which is nice in the hot weather that we always have in the UK.
I don't know if all C172s can be spun, but the ones I fly can, which might be a factor if you're into that type of thing.
The PA28, on the other hand, is nicer looking aircraft IMHO, which is very important!
The -161 can't be spun, although the -140 can. Personally, I prefer the low wing - much better visibility in turns. But as Evo says, this is a personal preference, and plenty of people prefer high wings (and if I'm taking someone sightseeing I prefer a high wing so my pax can see the ground better).
There might be other factors to take into account. For example, the club I rent from has some old PA28s - well looked after, but some of the avionics are a little tired, or missing altogether. The C172s at this particular club are brand new, kitted out with all the latest gear. The C172s cost more, because they are newer - but all this brand new kit is completely unnecessary for a new PPL (but very nice if you're planning on flying in IMC later on). It might be worth checking with Lancs whether there's any reasons such as this why you might prefer to hire one type of aircraft over the other.
Good luck!
FFF
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