If you don't want to mod, then your best bet would be the PS2 Independence exploit. Instructions can be found on this site.
As for the HDD itself, MOST IDE HDDs are compatible. Only a few have the connectors arranged in a way that causes problems due to the fact that the IDE/Power plugs on the Broadband adapter are solidly in place.
This option would also require the Phat PS2... Out of those, try to find the 50000 series. They're the most reliable of the old Phats. An easy way to tell is if it LACKS a firewire port on the front next to the USB ports.
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