For me personally:
1) Realized recently I don't seem to tolerate foods that have sorbitol in them, so I try to stay away from anything that uses those types of things as ingredients (green beans, apples, peaches, and a lot more). More testing still needs to be done to see which ones I might be able to tolerate and in what quantities, but I will be avoiding this unless testing. Once I have a definitive answer I will either avoid them entirely or eat very, very little!
2) Added sugar (sucrose) amounts, though it's usually not a deciding factor if I buy something or not. I try to control myself and almost never go beyond 25g of added sugar a day, so I don't decide whether to buy something based on that alone since I will almost always make sure I get below that amount regardless of how much is in that specific food. Even if it means separating it/eating half one day and half another or something.
3) The absolute biggest thing for me - artificial trans fats. x_x These are extremely bad for health and are slowly being banned or severely limited across the world. Not cool with the increased risk of cardiovascular issues. I will avoid anything that has them. Sadly in Australia most companies don't even list them since they're not required to, and in the US if a product has less than .5 they can list it as having 0. So I go through the ingredients to check for partially hydrogenated oils and other things that may raise red flags.