On the first page of the Investigator Story Guide it says this:
Finally, each investigator story guide lists the steps for choosing investigators and traits. Investigator players may wish to coordinate which investigators and starting equipment they choose. For exampe. investigators players may do better if they have both a smart investigator (high Intellect) and a physical investigator (high health and starting weapon) on their side.
The steps are always performed as follows:
1. Choose Investigators: Each player chooses an investigator and recieves the corresponding investigator card, Trait Cards, and listed number of skill point tokens.
2. Choose Traits: Each player chooses two of his investigator's Trait cards to represent his investigator's abilties during this game. He must choose one card with a "Strength" value and one with an "Intellect" value. He returns his investigator's other Trait cards to the box. He then recieves the Starting Item or Spell card listed on the chosen Trait cards.
3. Place Figures: Each player places his investigator figure on the Start space (as labeled in the "Map Setup" section)."
This should answer your question. You must choose one of each.