I guess the Action Replay Max allows you to backup savegames? If yes, you only need an official ps2 memory card and one ps1 game(only once). Look for indepence exploit in the guide. The independence exploit creates a special system config file that loads the .elf file you included in the process when you start the ps2 with the memory card and that specific ps1 game inserted. I recommend to put uLaunchELF in there, but putten the Free McBoot installer .elf there should also work.
FMCB should work on PS2 slim below SCPH9XXXX
as for independence exploit, it will only work with the fat ps2.
Unless you've already bought your PS2, I would recommend getting a used fat ps2 instead. It's much easier to install FMCB, since you can use independence exploit. Plus, you have much wider range of options rather than just swap magic (which you need to buy online...) and you don't have to worry about getting an unFMCBable ps2 since all phat are compatible with FMCB
but, if you insist on swap magic, then check their website. They have a list of trustworthy retailers who are selling swap magic.
there are over 50 millions PS2 consoles out there that ARE compatible with Freemcboot make sure you get one. Look for someone to install it for you locally if you can maybe post an add in free classified saying that youre willing to pay (be generous maybe half what you would have paid for swap magic/whatever you were going to buy)