Couldn't fit my whole question into the title. I want to make something that functions similarly to a ti84+ or a ti84pce with my own parts aside from the keypad matrix.

Should I start with a Pi Zero (yes I know it isn't a microprocessor but a full-blown computer) or a Pi Pico? This website shows the different specs of both, but I don't know how to interpret that for my needs.

Can both emulate a ti84pce OS? How far are the scripting capabilities? What differs from a standard ti84+ or ti84pce?
If you re-wrote TI-OS from scratch, I'm sure you could get it working on a Pi zero. However, that's not really feasible. Emulation is going to be significantly easier but require a much more powerful Pi. I started a similar project a while ago which used a Banana Pi (basically a faster Pi Zero W) instead. You'll want to take a look at it so you know what you're getting into:
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