Are there any cheaper screens that aren't touch screens? Also soldering in hdmi seems like a pain in the ass, and I'm sure as hell not gonna be able to fit a whole header in there. For battery solutions, I have heard good things about
these charging modules, and I was just thinking of a generic LiPo cell like
this. Or possibly using the battery charger board that is commonly used on portables,
this with two of those cells in series, I also saw one using a step of converter to get 5v from a single 3.7v cell (would that work well?). For a case, possibly something from small from polycase, then some frankencasing of DS lite button holes (and of course DS lite buttons). What do you think of these?
Screens:
RetroPie (I'd presume you would use it), and the Raspberry Pi in general doesn't really give a clear composite output. If you want to use a composite screen, then go for it. However, I do recommend a HDMI screen. Most of the small HDMI screens are marketed to work with the PI anyway, and they usually include a little adapter for this purpose. In short, If you buy an HDMI screen you won't have to wire HDMI by hand unless you want to.
Batteries:
This is where I think most Pi portables have their greatest weakness. Now, if you are using a PI ZERO, due to its wayy low power consumption, you could probably get away with using something as small as 1000mAh. But, if you are using a PI 2 or 3 you should definitely have 8000mah for a good 4 hour battery life. These cells can be hard to find, but
HERE is an option.
Battery Boards:
Don't make this more complicated than it needs to be. Systems for the Wii, GC, and N64 are very much different than what the PI requires. With an X number of batteries in a parallel arrangement, you can use the charge boards you already found and then
THIS step up board. Again, put the X parallel arrangement on a switch allowing the cells to connect to either the step up or charge boards. Connect the output of the step up to the PI and your barrel roll jack to the charge board.
Buttons:
No one else does this, but I prefer to use an off-brand Wii Classic controller for my buttons. You can get these really cheap, and they give you more buttons than any other commonly used donor.
HERE is one that I bought. I wouldn't however use the analog sticks, boards, and pads that come inside these controllers, as they are usually low quality. Place some tactile switches on some perfboard and use 3ds sliders instead.
Case:
Polycases, 3d printing, and vacuum forming are all viable options as long as you know what you are doing. However, another good method is to use sheet ABS.
1. Design the size of your box. You will need to know all 3 dimensions.
2. Trace your box pattern on your sheet ABS. Cut away all that is not to become your box.
3. Score the front side of the ABS. Gently bend the sides in to form the basic box shape. Be careful, as the sides can snap completely away easily.
4. Tape the four corners together. Using super glue, glue the inside seams of the box and then the outside seams. Tape can be removed after all the inside seams have been glued.
5. Sand the outside glue edges. The effect that you want in the end is a flat plane to bride the two sides together.
6. Trace all of the holes you will need to put in your new case for your controls, components, connectors, and etc.
7. Make the holes. Start by using a drill to remove large chunks of plastic, and then use X-Acto knives to remove plastic down to the edges of your traces.
8. Frankencase in your buttons from your donor.
9. Spray paint your case.