I was wondering on how to connect an EEPROM chip to the Raspberry Pi 3? And any suggestions on which EEPROM chip model is best to use with RPi3?
Most EEPROM chips use either SPI or I2C to transfer data, check the docs for the chip you choose to find out which and connect to the appropriate bus on the Pi. From there it's a matter of sending the right commands on the right bus -- again the chip docs will help with this.
There is, no doubt, many Python libraries to help with the commands (e.g. https://github.com/headamage/EEPROM-PiPython) or you could try the device-tree bindings for EEPROM chips: https://github.com/raspberrypi/linux/tree/rpi-4.19.y/Documentation/devicetree/bindings/eeprom
I've no specific experience on this but there might be a caveat: if you choose an I2C EEPROM avoid the temptation to use the second I2C bus, this is reserved for HATs.