I've used
Ubuntu 12.0.4,
Xubuntu and
Mint 13 (which is based on Ubuntu) on various laptops. The current trend in Ubuntu-land is for heavy-weight GUI desktops - Ubuntu's newer Unity desktop is quite different from earlier Gnome-style GUIs and seems to be fairly demanding in terms of memory etc. You can switch to the Gnome desktop in Ubuntu, which might be better for older/lower spec hardware, or Mint has a separate distribution with a Gnome-based desktop called MATE, which I prefer. Meanwhile, Xubuntu is another Ubuntu variant using the XFCE desktop, which runs fine on low-spec hardware e.g. I have it running on a netbook with an Atom processor and 2GB RAM.
So far I've found all these Ubuntu clones to be pretty stable and easy to install/use, and generally I like the Debian packaging system for installing extra software etc. Ubuntu and Mint both come with a shedload of applications such as LibreOffice, while Xubuntu is definitely a much lighter distribution - you get Abiword and Gnumeric instead of LibreOffice for example. I read somewhere that Ubuntu is easier to upgrade to a new version than e.g. Mint (where I think you basically have to re-install everything), but it depends if you plan to do this or not.
As Peter says, one problem might be with old hardware, and wireless
cards are a particular problem, e.g. I had an old Dell laptop which I tried to use with Linux but gave up in the end, because I could never get the wireless card drivers to work. But if you have a relatively recent machine (as an i3 probably is), you may well be fine.
Ubuntu (or Xubuntu) is easy to install e.g. in dual-boot mode, so you can try it before you commit to it. I'm running Mint in a VM, so I'm not sure how the dual-boot installation works for Mint. As Peter says, you can try out many Linux distros by booting from CDs/DVDs (e.g. from Linux magazines) without actually installing anything initially, so you can make sure your hardware works OK and get a feel for the various desktops etc.