I've done a fair amount of staining of pine wood, and have always preferred oil-base products over water-base. Never had a mold problem, either. A very good line of products is made by MinWax. Lots of colors to choose from, and I think they even make a sealer for outdoor applications. Used a water base stain on a picnic table/benches once, and it started flaking off within a year. Too much like a paint, not acting like a true stain.
I did an entire room with knotty-pine tongue-and-groove 1 x 6 stock, MinWax Puritan Pine color, installed at a 45 degree slope. Looked great for the 5 years I owned the place, and the buyers mentioned it was the main selling point in them wanting the house (along with the arched brick/stucco surround I built for the wood stove).