Don't get Ubuntu, it's really bad. It's super bloated, and it searches loving amazon before your own files in the dash.
On a really old computer, I suggest Lubuntu. It is so lightweight that it is able to run well on a Windows 98 machine.
If it's not
that old, then Xubuntu. It has a great ammount of customization with all of the functionality and support of any other Ubuntu based OS.
it really depends on the specs of the laptop. i installed ubuntu on an old computer, and some of the animations with unity (the desktop environment for standard ubuntu) were soooo sloooow. ubuntu is a really good choice for beginner linux users, but if you want something more like windows, check out mint. it's based off of ubuntu. later on, if you're wanting to try your hand at working with a minimalistic OS that's easily riceable without being too difficult for a newbie, consider crunchbang once you've got the basics of linux down. that's currently my distro of choice
No, not Linux Mint. It is going the same direction as Ubuntu, just less successful.
And for crunchbang, it's just debian with openbox and a few applications installed. If you want that, then just install debian yourself. It will allow you to learn the basics of how Linux works.
