Cello 500~3000
Violin 150~ 1500
Piano 5000~20000
Saxophone 1000~5000
Viola 400~3000
Drum group 1000~3500
Double bass 1800~4500
The price of each instrument is similar, generally 50~200 an hour.
What kind of piano to match should not be determined by height, but by what to use, but 175 is basically not difficult for these instruments.
If you want to solo piano > violin >; Saxophone > drum set
If you want to play the piano in a small band = drum set >; Saxophone = violin
If you are in a symphony orchestra, cello = viola = violin = double bass = saxophone.
It depends on your preference.
Besides drum sets, other musical instruments can be practiced at home, but saxophone is a nuisance, with a loud voice in the early stage. It's no use closing several windows. I used to learn saxophone, and then I played the piano.