If you're just getting started with TI-BASIC, but don't have other programming experience, I would recommend avoiding z80, as it's a whole other beast.
If you do decide to due to previous experience or a desire to crash your calculator/emulator very often, you can learn a bit at z80 heaven. It covers the basics with regards to calculators.
For a platformer, you'll probably want to draw sprites at specified locations (8x8 is a good size for assembly), implement physics (collision and gravity, gravity can be modeled as increasing downward velocity up to a maximum). A scoring system (time, coins, etc) may be desired, but should be less of a focus if you are just starting.