FreeMcboot will work fine on all Fat models. There are four different ways to play backups using FMCB: ESR patched burns, through HDD with network adapter(Fat only), through ethernet and through USB. Burned backups generally have the best compatibility, but HDD loading is very fast and lag free. Ethernet loading is very convenient as it allows you load games from any device on the network. USB loading however sucks pretty bad since the PS2 uses USB 1.1 which is not suitable for loading games.
If you need help installing FMCB on your memory card then I'm sure there are plenty of members here who would be willing to do it for you. I installed mine with the swap trick and I had to borrow my cousin's PS2 slim to do so as it's extremely difficult to do on a Fat.