Can someone send me an eaay guide on how to make a portable gamecube and list the supplies needed? (first time posting in like 6 months yay)

 

Wii U gamepad + Nintendont

 

You can't use the gamepad as a controller much less go places with it.

 

Buy a gamecube, buy an uninterruptable power supply, buy a screen, maybe buy a block of wood and buy some gaffer tape/duct tape or your preferred means of sticking one thing to another. Try not to block fans when you are sticking things together.

That is the easy guide, maybe step it up a tiny bit and buy a GC mod setup to dodge the drive related issues. Only way something you would actually want to use is "easy" is where you buy a kit off the shelf, maybe a shell in a pinch and if someone is making custom shells can you ask them to make some full size DVD supporting cases while they are at it.

More seriously
Step one is figure out what voltages are needed and what currents they need to be rated for, you might be able to drop it if you know what you are doing (the power supply will be rated for four controllers, plus GB player, plus memory cards, plus video, plus audio...). You then need to make this in batteries (most would use the classic lithium ion tool/laptop cells), as most things like this require fairly high current then I would not up volt and you will then need to make it. If the voltages are dropped again after the output of the power supply or the parts that require higher voltages are not used (the classic serial port on a computer might well operate at +-15V where everything else is likely to run at 12V, if you can lose serial for your computer build then you can dodge this). I am too lazy right now to go find one of my supplies or look it up but it should be on the back.
You then need a screen, best pick one with a voltage similar to what you are making for the GC. Car screens are good for this and usually come with nice inputs as well, that said I see your flag says US so you might well have a donor GC that is capable of having component done and there are now relatively easy to find kits/instructions for the component cables at least. I already mentioned the option of modding but I will mention it again, not sure what is out there for optical drive emulators these days but the SD adapters were doing well last I saw.
You then get the fun of making cases and redoing cables, not to mention sorting out a controller. Oh and the GC has a fan which is never fun for portable devices (no point in having the exhaust were your palm sits), not to mention the optical drive which probably does not like being jogged (no fun getting a disc read error because the bus went over a bump).

Here is a quick back of the envelope thing I did when someone asked about a portable N64, it is not going to be much different here in approach used. http://gbatemp.net/threads/why-cant-nintendo-give-us-a-nintendo-64.409979/page-2#post-5969980

 

Dolphin has 100% compatibility with gamecube games. They finally figured out the last kink in the memory allocator.