Eggs are one of the healthiest foods there are.
Cholesterol is a poor predictor of heart disease, at least at the gross level used by most physicians (if you dig into subtypes of LDL, different story, but even then just a correlate of more fundamental processes, a side effect, not the real issue). For example, many studies show that higher cholesterol is associated with increased longevity among people 60 and older.
Saturated fat is fine, assuming you aren't consuming it in the form of burgers and fries or pizza. That's another bogeyman, built on weak epidemiology, with dozens of uncontrolled confounds. It also violates anthropologic evidence that saturated fat is what we thrived on for millions of years and is responsible for our large brains. This myth is the detritus of Ancel Keys, who will go down in history as a villain and a fraud.
Nutritional "science" is upside down about so much. Maybe some day, the dieticians and medical profession as a whole will catch up. It'll probably be after we're all dead, though (alongside the millions they've already sent to an early grave with their advice), so it's best to do your own homework in this area.
I do recommend pastured eggs, if you can find them. Better than the generic grocery store variety. Less likely to cause allergic reactions (some people are allergic to components found in the egg whites), better treatment of the chickens, and natural chicken diet. Avoid "vegetarian-fed" eggs. Chickens aren't vegetarians. "Free range" sounds nice, but Big Ag has made it so the label is pretty meaningless. If the chickens are housed in a big warehouse the whole day, but they have a little door through which they can access a tiny area of grass, that's enough to qualify as "free range." "Cage free" is similarly meaningless.
p.s. I just got this in an email from my local rancher (from whom I get my pastured eggs). Thought I'd copy and paste here. He is clarifying what the labels mean:
"Free Range: according to the USDA only means the chicken is “allowed” access to the outside. They are still crammed inside buildings with a small door(s) that opens to a few feet of outside space. The sad truth is the hen does not know the door(s) exist because the chicken would have to know how to open the door(s). Many producers use deceptive pictures of hens foraging outside on their cartons.
Cage Free: simply means the hens are not in boxed cages. However, they are still confined inside very small and closed off buildings. They get no sunlight or access to the outdoors. They spend their day standing in their own filth.
Vegetarian Fed: well, the problem is chickens (like humans) are natural carnivores. It eats flesh to include bugs, insects, mice, etc. Hens are not vegetarians. This hen is raised on industrialized feed (probably GMO) and is never allowed outside.
Pasture Raised: is a term used by regenerative farms and means hens are raised outside on pasture. This is what you see when you read about hens in their natural habit."
The type to look for, then, is "pasture-raised."
