SEEPROM serial EEPROM?

Under that assumption, the "best" will be the one that suits your application.

I have, generally, used the ones from Philips (www.semiconductors.com)or ST (www.st.com).

If you look through the data sheets, you will - besides size - find 2 differences:
Max rewrites before data loss.
IIC or SPI aka microwire.

If you already use IIC for other purposes, use that, if not I would select based on price and performance and accept whatever interface the chip required.

As to code and power-up/power-down safety, use the search, this has been discussed many times.

Have serial fun,

Erik