88

88 beacause you'll get used to it.
Keyboards are great but 88 is what you'll encounter most.

the difference is that the place of middle c is different, and it's easier to learn on a full sized piano, because most songs are composed on a full sized piano, and have notes that go really high

I'd say start with the full-sized piano, cos then you won't have to get a new piano when you start to need the rest of the keys!
Trust me, finding the perfect piano for you takes time, and has to be done before you start taking lessons, and you get used to your first piano/keyboard, so it's best to stay with the same one the whole way through!

I would definitely recommend the 61 or 88 keys. You will quickly outgrow the 37 keys. Also, when looking at keyboards and digital pianos, it's important to look at the functions of the keys. Are they weighted? Are they touch sensitive? These will make big differences when you go from your keyboard to a real piano or even different keyboards.

37 keys is a definite no-no, that's like learning on a toy
If you think you'll keep learning piano for a few years, it's better to learn on a full sized 88 key piano (to get used to the feel, etc. keyboards always feel a bit lighter touch than piano) . By Grade 7 or 8 (Piano levels) you'll definitely need a 88 key piano, and not just that, there's a difference between learning on a keyboard that has the same dynamics no matter how hard you press it and learning on a keyboard that's louder if you press it harder.
I started off with the 61 key sound-the-same-no-matter-how-hard-you-pr… kind and switched to 88 key normal piano later at Grade 7 piano because later on it's not about the notes so much anymore : there's dynamics phrasing etc etc (and you'll need a real piano or one that can produce different dynamics)
hope that helps ^^