Puppy is around 50-200 MB
Ubuntu is a few gigabytes (I think 4 GB is bare minimum, 8+ GB recommended)
Fedora is 700 MB for bare minimum, 2.3 GB for normal desktop, and 6.9 GB for everything
Ubuntu is geared mainly towards typical desktop users with minimal Console involvement. Puppy is a lightweight Linux distribution geared towards older computers as it is comprised of the most basic programs to perform tasks. Fedora is like Ubuntu in that it is general purposed. I personally would recommend Ubuntu (you could use Xubuntu which is a very light-weight distribution of Ubuntu for older computers) if you are new to Linux because it is very user-friendly and has excellent support (good documentation and an simply amazing forum community). I don't know too much about the other distros so I can't really say much about them.