Well a CPU is not much good unless you can send instructions to it. They have to be stored somewhere, so you need memory. Now there are various types of memory chip and the most common types are RAM (Random Access Memory) which is fast, but forgets everything once power is switched off, and ROM (Read Only Memory) which keeps it contents after power down.
RAM is good for storing all things that change such as calculation results, the current colour of a pixel on the screen, the location of your pieces in a chess game. There are many uses. ROM on the other hand is fixed. The BIOS which is the program that initially starts your PC is stored on a ROM. It never changes. It can't change, and this makes it difficult to use in an experimental way because like CDs, once written at the factory, they can't be overwritten. We could use a PROM (Programmable Read Only Memory), but this is like a CD-R once you've finished writing to it, you can't overwrite or erase it either. There are EPROMS (Erasble Programmable Read Only Memories) but tend to need ultraviolet light to shine on them to erase them, hardly convenient. There is a better solution EEPROMS (Electrically Erasable Programmable Read Only Memories)
There is also a kind of half way house with SRAM (Static Random Access Memory) which is like RAM but will remember everything if you keep a low voltage applied as used by the BIOS to store settings and backed up with something like a CR2032 battery for when the power is switched off. They last for several years.
For my computer I am going to use an SRAM and EEPROM , which will effectively be my RAM and ROM.
The Z80 has 16 lines for addressing memories and 8 lines for the data. Back in the 80s, memories with similar pins were abundant but these days you have to go and hunt for them. I found some at Farnell's, it came to about £10 but I couldn't order with a credit card unless I bought £20 (pre VAT) worth of good, so I got 35 of each Red, Green and Yellow LEDs. The order arrived today - yay.
I got the ALLIANCE MEMORY AS6C1008-55PCN - SRAM and the ATMEL - AT28C64B-15PU - EEPROM. Need to read the data sheets and understand how they work so it'll be a while before I get going with these yet. The Arduino will help.