For softmod the better choice is to go for a phat model and not a slim. This is because only the phat can use an internal HDD and that is the most convenient method for playing backups.
Free Mcboot is the softmod method for allowing hombrew and game backups to be played. It is installed on a memory card and takes up a good chunk of space so you will likely want at least one more memory card for game saves. The easiest way to get free mcboot is to have some one install it on your memory card for you. The installer I believe has to do something unique to the memory cards address so you can not just use a PS2 to copy free mcboot, you have to run the installer and tell it what memory card to install it on.
If you can't find someone or a service to do it for you it is not that difficult. I did it myself. Basically you need a compatible PS2 game, for me I used Metal Gear Solid 3 Snake eater. The freemcboot site has a tutorial but basically I had to rip the game and use some software tools to replace a specific file in the image. I had to name it the same as the original file and burn this modified image to a DVD. Then basically I booted up the real game, opened up my PS2 to allow easy swapping of the modified disc. Then once the game is running from the backup I had to take the action in the game that executes the modified file, for MGS3 it was simply selecting the option to download camouflage and bam the file browser app launched, I picked the free mcboot installer and ran it and installed it to the memory card and have been good to go ever since.