Regardless of memory, the most common guts used by the boxes in the "under $50" price bracket are one of the following:
- Allwinner H618 (or H313)
- Rockchip RK3528 (or RK3506g2)
- Amlogic S905 (many variants)
What you will usually find is these boxes lack mainline Linux Kernel support due to proprietary drivers, though if you can live without hardware video decoding you can often get a 6.x kernel. That said, the Allwinner H618 stands out with full 7.x mainline support thanks to its predecessor the H616 (an older variation with a smaller cache).
Useful links: https://armbian.com/ | https://github.com/devmfc/debian-on-amlogic | https://github.com/ophub/amlogic-s9xxx-armbian | https://github.com/ophub/amlogic-s9xxx-openwrt
BIG CAVEAT: While some of the chips do support gigabit Ethernet and USB 3.0, you will unfortunately sometimes find that the gigabit PHY was omitted (i.e. you get 100 MbE instead), or no USB 3.0 port was exposed. 😓