Hello raygen88, welcome to LQ,
it depends on your knowledge of Linux.
In general the situation is that those distribution known to be very userfriendly come with big desktop environments like Gnome or KDE and therefore need a powerful graphics adapter.
Otherwise the distributions with the less hardware-requirements are less userfriendly.
But Ubuntu has a version with the LXDE windowmanager, called Lubuntu, maybe you should take a look at it.
As I wrote above, it depends on your knowledge, if you are already familiar with Linux you may want to try a distribution which is known to be less userfriendly. In this case it is relatively simple to suggest some which will run properly with your hardware, for example Slackware, Arch or Debian.
All in all the weak point of you computer is few RAM and probably an older graphics adapter. Otherwise the hardwaresupport for "older" computers is much better with Linux than with Windows. You will not have to expect issues with hardwaresupport.