Nuts don't give you high cholesterol. I don't think eggs do either. Cheese, maybe, since it's much higher in saturated fat.
Since I switched to a low-carb diet my cholesterol has come right down, but I eat loads of nuts and eggs - and oily fish, and olive oil, and rapeseed oil. Cheese too, but not massive amounts.
With meat, I tend to buy very lean cuts, then I can control the amount of fat (and how saturated it is) by the amount of cooking oil I use.
I'm convinced the obesity epidemic is much more related to high-carb diets than high-fat ones.
I think the most important thing is avoiding processed foods, there's no point giving up pepperoni's and eating cheese strings instead.
Yep, there's a lot of cr@p in processed food which just doesn't need to be there (including too much salt!)