Hi Adam,
The Cessna, e.g. C152 has a high wing - it is mounted above the pilot - so your view of the ground is unobstructed, apart from the wing support struts. The C152 is quite small and cramped - you will be literally rubbing shoulders with your instructor, and it only has 2 seats. I don't know if a C172 is any wider, but it does have four seats.
The Piper, e.g. PA28 is bigger and has a wing mounted below the pilot, so the view of the ground is obstructed quite a lot to the sides - not so good for sight-seeing. The PA28 has a larger cabin and is much more like a "real" aeroplane, whereas the C152 feels much smaller, more basic and flimsy, (but it is strong where it needs to be and is perfectly adequate - I started on a C152).
I imagine a PA28 will be more expensive to hire per hour than a C152.
They are both adequate aircraft for learning to fly. A C152 Aerobat can fly loops, I don't know if a PA28 is authorised for that.
If you learn on one type, you will be licensed to fly the other type - your licence will state SEP for single engine piston - but you should have some instruction, maybe a written test, and a test flight to ensure you know the differences. Things like critical speeds, operation of the flaps, basic handling etc.
I don't personally know the details about any other PPL types, but others here will be able to describe those. I only flew the C152, the PA28 and the Seneca twin before moving on to turbo-props and then big jets.
It really depends why you want to fly.
Enjoy, and good luck
