Pi Zero W GBA Display Options

[TechieAndroid]

I am making a Pi Zero W GBA and have had much trouble finding a proper screen for the project. I need a screen 2.8"-3.5" it needs to be powered by the Pi. Otherwise I will have to use the same battery that I will use for the Pi (haven't started looking for this yet) and just modify the power from it to the screen to make sure it gets the correct amount, I really don't want to do it this way but I will if necessary.

I don't know whether or not to connect the display to the HDMI (I will solder it if I use the HDMI option) or via the GPIO pins, I would like to know the specifics of using the GPIO pins for it (like will it look okay for playing GBA games, color depth and resolution wise? ).

So far here's what I've got going:
I have a brand new working GBA which I plan to use the shell/case and part of the board (the part for the buttons) unless I decide to send off and have custom PCBs made for that, I'm still thinking about this. I'm planning on using the Pi Zero W for it's size and wireless capability (I plan on keeping it inside the gba at all times).

Total Parts:

GBA
Pi Zero W
Screen
Battery

Here's the original GBA screen specs:

Screen: HQVGA 240x160 3:2 2.9 inches

Color support: 15-bit BGR (5 bits depth per channel), capable of displaying 512 simultaneous colors in

"character mode" and 32,768 (215) simultaneous colors in "bitmap mode".

[TechieAndroid]

Here are the current displays that I have found. Let me know what you think.

PiTFT Plus 480x320 3.5" TFT+Touchscreen for Raspberry Pi

PiTFT Plus 480x320 3.5" TFT+Touchscreen for Raspberry Pi - Pi 2 and Model A+ / B+

For Raspberry Pi 3 2 TFT LCD Display, kuman 3.5 Inch 480x320 TFT Touch Screen Monitor for Raspberry Pi Model B B+ A+ A Module SPI Interface with Touch Pen SC06

[obsidianspider]

I'm working with a 3.2" Sainsmart/Waveshare clone that seems to fit pretty well with trimming.

[TechieAndroid]

Moving thread now that I see the Projects and Themes section (I was looking for a section like that before posting but got confused by this site's layout).