Small system on a chip : Power consumption
First work on your specifications.

An 8-bit microprocessor?? That is weird. Why the fix on 8-bit? And then, why a microprocessor and not a microcontroller?

memory: RAM? ROM? FLASH? How much? 

display: what do you want to display? Can it be reflective or does it have to produce light? (for low requirements + reflective this is probably the least problematic part of your design). 

communication: if this must be on all the time it is likely to dominate your power budget. Consider all alternatives, including simple transceivers and less-than-100%-on scenarios.

Battery: every design must have one 'free variable', this is likely yours.