The green ST7735S display should be fine. Likewise all the other 128x160 ST7735 displays.
The green pcb has a microSD and all the pins in one line.
The Red and Blue pcbs tend to have a big SD cage and separate pins for the SD.
The 128x128 boards do not have an SD.
All of these displays require 3.3V logic. Do not believe Ebay adverts.
If you can post a link to your "poor Chinese display", we can probably get you going.
Yes, an SD or microSD is handy for prototyping. If you are going for ESP32, it is not needed.
Regarding SRAM. LZW needs 16kB. The imageData[] and imageDataBU[] arrays each need W x H
bytes e.g. 76kB for 240x320.
My STM32L476 has got 128kB SRAM. I can render 160x160 GIFs.
My Teensy3.2 has got 64kB SRAM. I can render 128x128 GIFs.
If I can avoid imageData[] arrays in SRAM, it comes down to "GIFs can work with a 20kB SRAM controller". I need to get my head into gear before I see how/if this can be achieved.
David.