The one thing you might have problems with is your wireless card. I have had issues off and on with the wireless in my old HP laptop, but the latest versions of Ubuntu and Mint seem to handle it just fine. Most other hardware is usually not an issue. (My laptop even has a mobile nvidia card and the native drivers that Ubuntu/Mint loads after installation work just fine.)
Also, most distros are bundled as live CDs. So you can try the distro by booting from the CD and see how it works.
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.