am thinking of buying a second hand gamecube from a shop

can i play emulator on there like with the wii homebrew channel

There are methods of launching homebrew on the GC, such as using an Action Replay and the cheat code "SD Load" or something like that and an SD Gecko.

Or you can use the "GC Homebrew Launcher" from Datel (same people who make Action Replay) : [uk.codejunkies.com]

Or you can use a modchip, or there is I think an exploit for Phantasy Star using the Ethernet adapter (probably the most complicated method).

Easiest is probably "GC Homebrew Launcher"

The PSO hack is long and ridiculously complicated (you need like 10 pieces of software!); I looked into it so I know. I was pretty much wondering the same thing. Also is there a game exploit that would work with a USB Gecko or something like the Bannerbomb hack for Wii with a USB Gecko?

No. I am 99% sure there is not. The easiest way is just to buy an SD Homebrew Launcher from Datel.