Both Mint and Ubuntu are good starting points for a Linux OS.
Mint min. specs are:
512MB RAM (1GB recommended for a comfortable usage).
9GB of disk space (20GB recommended).
Graphics card capable of 800×600 resolution (1024×768 recommended).
DVD drive or USB port
Ubuntu min. specs are:
700 MHz processor (about Intel Celeron or better)
512 MiB RAM (system memory)
5 GB of hard-drive space (or USB stick, memory card or external drive but see LiveCD for an alternative approach)
VGA capable of 1024x768 screen resolution
Either a CD/DVD drive or a USB port for the installer media