Given a star's mass, age, and composition, how do I calculate the rest of its properties? If I'm given a star's starting mass, starting composition (metallicity), and its current age, How do I calculate the star's luminosity, current mass, and radius?
I want to know how to do this for any star, from the minimum size of 0.08 solar masses all the way up to stars 100-150 solar masses for a personal project.

I know that there are equations that relate these things, but my desperate googling has only found bits and pieces of the answer I'm seeking. Also, many of the equations I've found only apply to stars within a certain mass range (usually near the sun.)
I would seriously appreciate some guidance from an expert in the field.
In astronomy research, models of stars are computed using large software packages that solve a set of differential equations that describe the structure of a star as it evolves, mostly because of nuclear fusion transforming elements, under a number of assumptions.  (I once wrote a more detailed answer about this on Physics.SE.) So I'd say the first option is to find and operate one of these programs. One of the easiest to access and use is MESA but there are many others that exist, although they often aren't freely available.

Another option is to use (probably by interpolating in) large tables of models that have been produced using those codes.  MESA is used to produce the MESA Isochrones and Stellar Tracks for which the isochrones Python package provides an interface, but there's also the Dartmouth Stellar Evolution Database and the PARSEC grid, among others.  (Apologies to all the isochrone grids I've missed!)

You can also try your hand with the program SSE, which uses analytic fits to a grid of models from the late 1990s. While SSE implements them, the analytic fits themselves are described in Hurley, Pols &amp; Tout (2000).