If ease of use is prime concern and 'easy' means fully automatic here, I'd second sudodus's last advice -
The solution in the thread he linked to is basically offers the same thing that 13.10 will offer you - the driver from kernel 3.12.. You can install the latest kernel in 12.04 too, which will be offered the upgrade to 14.04 (or just its kernel and Xorg packages only, as and if required) anyway. So you can choose whichever seems to be the best working solution for you -otherwise go for 13.10 and hope it will be easy to upgrade to 14.04, which will be an LTS release.
1) Install the latest supported kernel on 12.04.3, which will install the same driver which you would have otherwise compiled from the backports package. This will be a permanent fix with no need to compile anything or do anything manually later. But whether the overall system would perform better after this upgrade can be questionable.
2) Install 13.10 and upgrade it to 14.04 when it comes out. I'd personally recommend to do the upgrade about a month later to give 14.04 enough time to iron out its bugs. Be aware that an 'upgrade' is not always smooth and sometimes breaks features/functionality/entire installation, especially if you are using any proprietary drivers and software from ppa's.
3) The above concerns bring up a third option that can be considered - Install 13.10 now, keep data in separate partitions (creating a separate /home partition makes that smooth and safe), and do a fresh install of 14.04 when it comes out.
Of course there are also some other options in-between, but none as easy and smooth as above ones.
Oh, and don't forget to test 13.10 in live mode first to make sure it works well with the hardware.