I think you are making this harder than it needs to be, to be perfectly honest. When you are first considering a product, look at the allergen statement at the bottom of the ingredients ("Contains" part). Right away, if it says eggs, dairy, or milk products, you can rule the product out fairly quickly.
If none of those are mentioned, go ahead and read through the ingredients. The main ones you need to look out for: D3, honey, milk, eggs, glycerin, mono and diglycerides, casein, lactic acid, stearic acid (or any derivative of stearic), and l-cysteine (usually a bread conditioner). Natural flavors can be questionable as well, but I tend to give a little more leeway for those when I "know" the company. If you are ever scrutinizing a label and cannot decide whether to buy it or not, call the company and ask! That's what the little number on the side of the box is for.
Like Jen said, though, stick to more simple products. You don't need any of the foods that have 20+ ingredients. The main packaged foods I buy are food bars, cereal, and bread, and for those days I can't cook, I keep some Amy's soup or packaged Near East rice on hand.
Also, read the label to the best of your ability, and if it seems alright, it should be fine. Don't stress about it too much or you will discourage yourself from staying vegan. It is also harder in the beginning as you learn which products are suitable and which ones are not, so hang in there!