I have version 12.0.76.3 and I need to reinstall, how can I tell what distro I need to download?
For FreePBX 12 you are looking for Distro version 6.12.65
http://downloads.freepbxdistro.org/ISO/
This version is end of life, so you really want to upgrade to current when you can:
http://wiki.freepbx.org/display/PPS/FreePBX-Distro-6.12.65
Can I do an in place upgrade to the latest version or can I install the latest version and restore from a backup of my current PBX?
You can only restore backups between like versions of FreePBX, a 12->13 restore WILL fail. With any modern version of the FreePBX distro you can upgrade in place using the scripts linked above.