For the Cessna vs Piper debate, it depends on whether you prefer to bash your head or your legs
There are other aircraft sometimes used by flight schools like the Tecnam's and Diamond DA40's, but C152, C172's and PA28's appear to be the most common used.
I've predominantly flown a C152 and C172 for my PPL. Big advantages are visibility of the ground which is nice for sightseeing, but you can't see very well when turning such as when you're turning to final, but it's not too big a deal.
C152's are probably the cheapest aircraft you'll come across for learning on, but with two adults you might not have such a great range as there's a fair chance you won't be able to carry full tanks of fuel because of the weight. If you and your passenger are fairly slender, you might be able to though. Some have long range tanks which will give you around 6 hours flying time, but unlikely you'll be able to take anyone with you when carrying that much fuel.
The C172 is a bit faster and more practical for longer trips what with the extra space and capacity to carry fuel etc. The C172 is easy to fly and the C152 even more so.
My experience with PA28's if fairly limited, but if you do decide to move beyond a PPL, a lot of flight schools still use variants of the PA28 for their commercial courses, so you'll probably feel right at home stepping into that. It also feels like PA28's are a bit more abundant in general.
Ultimately, they're all great training aircraft and different people will have different preferences, but these are the main things I've observed.