Any water that gets to the inside of the window has the potential of running down the walls and eventually rotting out the structure (plus getting the basement wet). Even one drop every so often over time can cause serious problems. Even the steam condensation from the shower can cause mositure problems and drops of water pooling along the inside sill.
The plexiglass with sealant around the entire frame would work the best, and may not be too unattractive. Another alternative is to run a rod along the wall and pull a shower curtian back during each shower.
Another alternative is to enclose the opening altogether, or at least put in a higher window that wouldn’t get direct spray from the shower.
I’m running out of ideas. If it were my house, I’d either remove or replace the window.