If you are looking for a non-chemical, mineral sunscreen, you could do a lot worse than GM Collin Mineral Sun Veil SPF15
($28 for 4oz). The active ingredient is zinc oxide at a concentration of 12.5%. There's a fair bit of silicone so, unlike most mineral sunscreens (you know that chalky feeling), it is non-greasy, but silky. There are also a couple of nice botanicals, such as fumaria officinalis, with a pedigree of skin benefits. Plus some vitamin E.
Unfortunately, there are a couple of things that I'd rather not encounter. But, then, a sunscreen that works and is free of nasties is very hard to find. In the case of Sun Veil, there is PEG-10. PEGs typically contain impurities that can irritate broken skin. Possibly worse is sodium benzotriazolyl butyphenol sulphonate; this is certainly toxic, but one imagines the concentration here is too low to be harmful.