Changes and new impulses will definitely improve you as a musician.
Should you go for piano/classical/crossover, I cannot tell you that.
It very much depends on what you are looking for.
The crossovers have radiused fingerboard and are mostly used plugged-in, hence tone production is not as important. Often they are 14-fret instruments and lack the sweetness of a typical classical guitar.
Classical guitar will give you a whole new spectrum of repertoire to choose from. And may want you to dive deeper into its own domain. More so than a crossover.
As for prices... my first classical was ca $500 , all solid instrument. Good enough to let me develop my skills and reward me for the time invested.
Definitely go all-solid and an instrument that can handle hard tension strings. Have it set up properly, so that tone production can really be made.
__________________
Nylon string are softer, but harder to play 
Alhambra 11P
|