Hi, welcome to the forums! I built a G-Wii for my first portable as well so I feel like I should be able to help you out somewhat.
You’re going to need quite a few tools to get started in portablizing. The most obvious being a good soldering iron, I wouldn’t skimp out and get some Chinese shit, go for a good Weller soldering iron, or the Hakko FX888D if you can afford it. Something with temperature control is ideal. You’ll need plenty of wire to make connections between things. The connections between cells will require 22 AWG gauge wire, whilst you will want some 38 AWG magnet wire for Bluetooth and other data line connections. I personally like using 30 AWG kynar wire for things like audio and GC+ wiring as it’s easy to route and keep things neat inside the case.
As for using shielded wire, I usually will twist magnet wires in pairs with ground to reduce interference on the video and audio lines. I recently did this on a portable I was building and had absolutely no interference at all. Magnet wire has an enamel coating and is very thin. You can simply strip the coating by heating the wire back and forth in a solder blob on the end of your iron to expose the copper. Highly recommend this stuff. You’ll need it if you want to relocate the Bluetooth module, as those traces are very very thin (0.1mm iirc).
You don’t necessarily need the case to start portablizing (obviously you verify a working wii trim with just a power bench supply, or with batteries, PMS and regs) so it’s not 100% necessary to get started with the case, although I don’t see any reason not to have the case on hand.
A hot air station can be really useful for SMD rework but it certainly isn’t necessary to put together a portable in my opinion. Finally, other miscellaneous things you will find useful are things like tweezers for wire routing and holding wires, flux for soldering to Wii vias, solder for soldering (duh), wire strippers, cutters, and finally, I’d recommend getting some soldering braid as well which makes removing solder a breeze if you make any mistakes.
Obviously you’ll need a BOM of components as well to build the G-Wii, but Gman has posted a list of parts in his original post you can use. I’d recommend also watching Noah’s YouTube live-streams as well, and checking out the internals of the G-Wii to give you a better idea on the build process and the order of operations to get a feel for the build.
Good luck! I remember starting out and there’s a lot of things to buy at the outset, but if you make a small list it’ll help you keep track of all the things you need to get started.