A Linux live disk is a CD or USB drive from which you can start your computer. If you have a USB drive with enough free space you can install a linux distribution on it. The advantage of using a USB instead of a CD is that with a USB you can choose to create a persistent system which means that you won’t have to reinstall everything if you need to reboot.
Which distribution you choose doesn’t really matter. I use Ubuntu because it’s the most used distro and there is therefore a lot of support for it. Knoppix is very popular for live disk use, but I have no experience at using it.
If you follow the instructions here, you will probably be able to create a linux disk:
To start from the Linux Live CD/USB you have to enter BIOS and change the boot sequence and put your CD drive or USB port at the top. Then reboot your computer with the CD/USB inserted.
The next step is to install the programs you need. If you choose Ubuntu you can find them at Applications -> Software Center. Search for “testdisk” and click “Install”. This will install both TestDisk and PhotoRec.