In general, I would recommend always going with the latest version of Ubuntu as (in general) it's going to be the best optimised for the widest range of hardware, even older hardware. That or the latest LTS (long term support) version if you'd rather not upgrade more than every 2 years.
The only exception would be if your hardware falls significantly below the recommended minimum stats for the latest release. In which case, instead of installing an older version of Ubuntu, I'd recommend opting for a different distribution.
Ubuntu (and most Linux distributions) can run on a surprisingly low specced machine. 512MB RAM and a 20MB hard drive, for example, is absolutely fine (and I even run full graphical Ubuntu in VMs with these specs).
Your system is more than enough to support Ubuntu, and probably many future versions of Ubuntu too.
I wouldn't go installing an old version of Ubuntu specifically to better support old hardware. If you pick a version that is no longer supported, you are leaving yourself vulnerable to known security vulnerabilities which are patched in later versions.