The fact that you ask this question first before posting in the Introduce Yourself section (which then you will get a reply with helpful links) shows me that likely you haven't yet used our modding guide (Softmod Any Wii), so I would start there to make sure your system is current.
Then there is FAT32 guide to get your hard drive ready, and yes, you can play Wii and GC games off the same hard drive once you've set this up properly. You'll want to format with 32k clusters for gamecube games to work.
Then there are Dios Mios and Devolution as two methods to run GameCube games.
All guide mentioned above are linked in my signature.