Fermentation – Best Weights to Use for Fermenting Sauerkraut

The ingredients of sauerkraut are very basic--its basically just cabbage and salt (the water is drawn out of the cabbage). Given this, you will produce the most nutritious kraut using high-quality cabbage and salt with natural minerals. A high quality sea salt will contain additional minerals that processed kosher and table salts lack (also, it is typically advised not to use salt with iodine--as it apparently prevents the growth of the desired bacteria). Additional ingredients such as spices will add their relative nutritional value to the mix.

Obviously this doesn't necessary maximize or preserve any "probiotic" aspect in particular, but as commenters have mentioned these claims are dubious as best.

Also, by the way, you only need to add water if the cabbage fails to produce enough brine to cover it after being salted. If you do add water you'll want to add additional salt so as to preserve the salinity--typically I've used 1Tbsp of salt per quart of water.

Any salt will work just fine, salt is salt. But salt that has had iodine added (table salt) can result in a brine with a cloudy texture. Some might consider this less aesthetically pleasing.

Edit:

Further research indicates that while iodine can cause some problems, other impurities can cause further problems:

Salt for pickling:

For pickling any variety of common salt is suitable as long as it is pure. Impurities or additives can cause problems. Salt with chemicals to reduce caking should not be used as they make the brine cloudy. Salt with lime impurities can reduce the acidity of the final product and reduce the shelf life of the product. Salt with iron impurities can result in the blackening of the vegetables. Magnesium impurities impart a bitter taste. Carbonates can result in pickles with a soft texture (Lal, Siddappa and Tandon, 1986).

So in summary look for a high concentration of Sodium-chloride (NaCl) vs other ingredients. As another answer states, it seems kosher salt is an excellent, reasonably priced choice.