Need advice on the `range` of some instruments.

I am kind of inventing an instrument and I need some advice on the range I should pitch it at.
The instument will have just about exactly 3 Octaves in range so that's not much. I want to make more then one version, a bit like a recorder so that it can be used for different parts.
Could someone who is familiar with differently ranged instruments please advise me on some ranges that I should settle on. The intrument will be single note like a clarinet or violin rather than multi note like a piano and I hope that it will be ideal for playing poppular tunes.
Do you think the example of the various recorders is a good one to follow. They have different ranges from Bass to Sopranino but with the soprano being the standard one most people learn.
If an instrument has only 3 octaves then for playing both classical, traditional and poppular melodies then what would be the ideal starting and top note, range for this instrument?

Hope to hear everyone's advice.