Hello, stillyx3, I can't really help you, because I'm not a professional portabilizer, but one day, I wanted, just like you, to build a portable Gamecube. Some people told me it was pretty hard and I must say - it's hard for a first - but if you are determined to make a portable Gamecube, then that's what you need to build. To be honest, the only way to learn soldering is to try soldering things. Also, I think there are some tutorials on the Internet.
Back to the portable Gamecube. I've started one too, here's how I've proceeded :
1- Get a plain Gamecube mobo with a minimal trim - final result (just remove the gold edges) :
http://origin.arstechnica.com/staff/fatbits.media/images/gc-mobo-small.jpg
2- Get a case. That's really important and before ordering or creating any case, you should measure your mobo.
3- Get a screen. Once again, that's more or less linked to your case dimensions. The size of your screen depends on it, so be careful. Ebay's 12v car screens work perfectly !
4- Get an amp, and speakers. DS Lite ones are pretty good.
5- Wire needed things to make the GC working. =Wiring the screen, and the audio part. Once you've done that, just try to put the mobo in your case, just in case it wouldn't fit anymore.
6- Wiikey Fusion ! I'm actually at that step, so I can't really explain you, but the Wiikey Fusion is a chip that allows you to remove the disc drive and play backups from an SD card. that's really important for a portable GC, but also very complex to wire for me. I'm actually trying to wire one.
I hope this will help you, and if it doesn't, this link will surely :
http://kyorune.com/modding/article.php?id=84. This is a pretty complete guide to portable gamecube, and caseworking.
Also, I'm terribly sorry for my English.
Uly_