Question: Given a piano music sheet, is there any way to know which (suitable) octave should I start, or I just pick up any as long as it fits all notes? 

Sorry if this is a dumb question! Thanks

Answer: 
Standard sheet music specifies the octaves quite precisely. The lowest line in the treble [clef](https://en.wikipedia.org/wiki/Clef), for example, is E4 (the E in the fourth octave):

[![e4 note](https://i.stack.imgur.com/gMcy7t.png)](https://i.stack.imgur.com/gMcy7t.png)

[Ledger lines](https://en.wikipedia.org/wiki/Ledger_line) can also be added above and below the [staves](https://en.wikipedia.org/wiki/Staff_(music)) to extend their range, and you might sometimes see *[8va](https://en.wikipedia.org/wiki/Octave#Notation)* written above or below certain notes to indicate that they should be played an octave higher or lower.
Generally, the pitch is fixed. However, if you are playing music for other instruments, there may be some justification for adjusting pitches. For example, guitar is usually written one octave higher than it is played (when written correctly, an 8 below the clef indicates the shift). However, its bass notes tend to have an "unmuddier" sound than that of the piano, so there is some sense in playing it as if it were not written transposed.

Similarly, a soprano recorder (flute) tends to be written one octave lower than it is actually played (with tenor recorders (flutes) being written in-pitch if I remember correctly). Again, the sound quality of the piano may make it advisable to play the music as if it were not written transposed.

Music written for piano, however, is always to be played at pitch. The "middle C" C4 between treble and bass clef is pretty much in the middle for pianos. If your piano has a lock, it will be rather close to middle C.