Is there a positive synonym for "indecisive"?
analytical:
skilled in or using analysis especially in thinking or reasoning
deliberate:
characterized by or resulting from careful and thorough consideration
characterized by awareness of the consequences
judicious:
having, exercising, or characterized by sound judgment
A few more options: rational, prudent, sensible.
I would suggest meticulous.
Meticulous suggests that someone is gathering information to ensure that all details and options are covered. This can be a result of acting methodically or otherwise.