Picky (Merriam-Webster), as you know, generally has a negative connotation because it is implied that picky individuals are may be generally hard to please, and they may lack static, well-defined standards for being so selective. As Merriam-Webster puts it in their definition for fastidious (another word you might consider, though will likely want to reject), they have "capricious standards." We also often use this word to describe children. Having said that, a number of other brands have actually "owned" the word "picky," proudly admitting that they are picky about their ingredients, some even going so far as to include the word "picky" in the name of their product. It sounds like you want to set yourself apart from those brands by using a more mature-sounding word.
For me, the first word that comes to mind that fits this bill is discerning, which user Okoning as already graciously suggested; however, with a little thought, a few others came to mind.
You might consider meticulous. This shows that you are painstaking, precise, and thorough about every detail (American Heritage® Dictionary of the English Language) when you select your ingredients. As person who is sometimes inappropriately meticulous myself, I may be especially partial to the word. A quick search of the web shows that some makers of food and cosmetic products are comfortable with this word and already use the exact phrase "meticulously select our ingredients."
Persnickety can conjure an air of fussiness (Random House Kernerman Webster's College Dictionary) and snootiness (Wordnet 3.0) that, depending upon the image you want for your product, may not be a bad thing. If the word fits the rest of your description, prospective customers may be happy to hear that you care, to a fault, about what goes into your products.
I feel compelled to present a short B-list options as well:
We're zealous about the ingredients we use.
On one hand, you may want to show off your unbridled enthusiasm (Collins English Dictionary) for your ingredients. On the other hand, thanks to the word's informal meanings (The American Heritage® Roget's Thesaurus), this may make it sound as though, when you receive ingredients that don't meet your standards for freshness, it is company policy to smash the tail lights of the truck that delivered the offending produce.
We're methodical about the ingredients we use.
By itself, I don't think methodical has the punch you are seeking. If you augment it with "yet X," it might work for you:
We're methodical yet passionate about the ingredients we use.
or methodical yet discerning, etc.
This makes it sound more like you only select an ingredient if it gets a favorable report from your lab coat-wearing, clipboard-toting experts (American Heritage® Dictionary of the English Language), and is declared "finest in the land" or at least "not complete rubbish" by your monocle-and-ascot-sporting aficionado.