What are the required parts for an 8-bit computer?
The absolute minimum of parts you need is just the 65(C)02 CPU and a handful of resistors. It's possible to pull the data lines up/down to always read as a single value (e.g, 0xEA, the NOP opcode), causing the processor to run that instruction endlessly. Information on this trick can be read here.

Running any real program will require somewhere to store it, though. So you'll probably want an EEPROM.

Any meaningful program will need some RAM, so you will probably want some SRAM. Selecting between the two will require some sort of address decode logic. There are a number of ways to implement this, but probably the easiest is to use logic gates on the top few address lines to generate chip enable signals for the SRAM and EEPROM chips. (For instance, for 32K RAM / 32K ROM, A15 could be used directly as a chip enable for ROM, and ~A15 for the RAM.) More complex address layouts may merit the use of a PAL for address decode.

You will also probably want some way of communicating with the world. How you do this is up to you; some easy options include:


An 8-bit register with some LEDs hooked up to it
Serial communications, using the ACIA (65C51)
GPIO, using the VIA (65C22)
An HD44780-compatible LCD


Any of these options will require that you reserve a range of memory for the peripheral in your memory decode logic.