BJT switch: Exact base resistor to limit current, or allow more current than needed & then use a current limiting resistor?
Use a current limiting resistor. Beta is highly variable, so you can't really rely on it for setting collector current.

Usually when you switch an LED, it is a saturated switching application. So you assume Vce will be around 0.2V (or use Vce(sat) from datasheet). Pick a current limiting resistor for the LED based on the typical Vf of the LED. And use a design beta of 10 or 20 to calculate the base resistor value for the BJT.

You can also use a small signal MOSFET such as a BSS138. Then you don't need to worry about base current.