Make sure that the new distribution supports the storage that you've set up, including
- partitioning type (PC, UEFI, …)
- RAID or encryption layer (mdraid, dmcrypt, …)
- volume layer (LVM, …)
- filesystem (ext4, btrfs, zfs, …)
Going from Ubuntu 12.04 to Debian wheezy or even squeeze, I don't think you'll lose anything, so in your case you won't run into any problem.
Be sure to back up
/etc from your Ubuntu installation. In particular, you'll need to restore the user and group IDs from your existing installation, for all your users that have a home directory in
/home. Files are associated to user and group IDs, not names. The association between user IDs and names lives in
/etc/passwd, and for groups in
/etc/group. If you copy entries from your backup to your new system, be sure to copy the corresponding entries in
/etc/gshadow as well.
If you want to retain your machine's SSH identity, copy
/etc/ssh/*key* from the old installation.
If you've set up LUKS disk encryption with a key file, be sure to keep the key file.
Whether to choose stable, testing or unstable is up to you, it depends how much you value security and stability vs having the latest software (complete with the latest bugs).