While historically a major part of the cost of an 8 bit computer would be high density RAM and ROM, this stuff is relatively cheap, and can even still be bought from suppliers such as Digikey.
If I was starting from scratch, I'd start with a 28C256 EEPROM and a 61256 or 62256 SRAM, which can be sourced on places like eBay easily enough in a DIP package as well.
https://www.digikey.com/product-detail/en/microchip-technology/AT28C256-15PU/AT28C256-15PU-ND/1008506