Known brand name
Generally speaking, if the brand name is known (MAC, L'Oreal, Revlon, Urban Decay, Stila, Make Up For Ever, and I could go on and on), it can be a sign that you can just go ahead and purchase. Pretty much anything that you'll find at Ulta or Sephora will be brands that you can count on being good brands.
That being said, it's not completely fail safe either. Near 15 years ago, I developed an allergy to L'Oreal products to a point where I couldn't wear my contacts, let alone any makeup, for like a week. My eyes were extremely puffy. I had been using L'Oreal products for years without any problem and this suddenly developed. I'm not saying that L'Oreal makes bad products but just that, even when you've been using a product for years and it's well reputed doesn't mean that it's fail safe.
Little known brand names
There are a ton of those out there. What prompted me to write this blog post is that I was looking for glitter yesterday and found a new brand that I had never heard about: Medusa's Makeup. (I'll post a review once I receive the products.) So what do you then? Well, unless you have super easy going skin and eyes, you want to look into product reviews before purchasing. It's as simple as doing a Google search for the brand name and review (so, in this example, I typed in "medusa's makeup review"). You'll generally find blogs and youtube videos telling you what they think about the brand. They will often have swatches too that you can see about what they received so it gives you an idea of the pigmentation level, which can come in handy. So ready about what people say about it and make up your own mind as to whether you want to invest or not.
Pricey does not mean better
Just a word on price: it's not because you pay a ton for something that it will automatically be better. Nor is it a contest of the cheapest makeup. Each vendor prices as they see fit so don't let price influence your decision when making a purchase. If it's dirt cheap, though, you need to be cautious as it may be cheaper quality products. But like NYX products are super cheap but they work very well, I gotta tell you.
It's really a crap shoot
In case you haven't figured that out from this blog yet, there's really no easy way to figure out whether a product will work for you or not. For all that folks can rave about something, it may not work for you. So, as such, you may not want to invest a boat load of money in one brand only to discover that it doesn't work for you. I have been using a ton of different brands, including some cheaper ones (in terms of price) and, since the L'Oreal incident, I've never found anything else that has created an allergic reaction for me and I have very sensitive skin and eyes.
If ever you do find products that don't work, do take the time to look into what the ingredients are: you may eventually find a trend where products that contain XX component make your eyes react.
Still, I strongly believe that doing your due diligence and reading the reviews online about products will help you gain a better idea of what you would be getting.