What level will your new character on destiny be if you have already completed one or two of them?
Solution 1:
Each "new" character you create will be level 1 like before, and You will have to go through story missions again. there is a few "new" features you will have available to your new character, though.
Firstly, if your first character is level 15+ (yes, in your case), you will be able to switch between subclasses freely on your new character. EX. You could start as a Defender.
Second, all of your glimmer is shared between characters, so buying gear for your new character will be a bit easier.
Third, the Vault is shared between characters as well. if you got a nice item for a different class that you plan on building, go ahead and vault it for them!
And finally, weekly and daily missions are bound to the character, so you could effectively double and triple your strange coin/ascendant farm if you have all three characters strong enough.
Solution 2:
Yes. Each new character you create, regardless of class, starts over from the beginning again. Level 1, no gear, no skills.