Lactobacillus acidophilus is probably your best bet. It's a fermentative bacteria, is considered a probiotic, and using it results in a sour milk with an even, palatable flavor. The upside of using acidophilus is that you can buy it from the grocery/drug store in tablet or capsule form. I'm not sure about regional availability, but my local HEB has cold-kept acidophilus culture available for purchase which I have used in the past to make acidophilus cheese by fermenting at relatively high temperatures (though Streptococcus thermophilus is honestly better for making cheese). Alternatively, you can just put a scoop of fresh live-culture yogurt in your milk, which will work just as well.
Keep in mind that the temperature of fermentation will affect the consistency of the finished product. When making acidophilus cheese, I kept the temperature near 100°F for nearly a day. According to this wikiHow article, adding the culture to 115°F to 120°F milk and allowing it to set up for 6 hours will produce yogurt. This leads me to believe that adding the culture to milk at a lower temperature and letting it set up for a shorter time will yield soured milk that isn't thickened to yogurt levels. Since acidophilus doesn't require curing, you can just taste the milk as it sets to determine how sour you want it to get.