I'm neither a vegetarian nor a doctor, but my (limited) understanding is that saturated fat is what raises LDL cholesterol. So, cutting out cheese, full-fat dairy, and butter should go a long way towards bringing LDL down.
Can't help you with the soy questions. I'm interested to see what others have to say, as it wouldn't hurt me to east some tofu every now and then.
EDIT: Dr. Google turned up this page, which I found useful: http://www.lowfatlifestyle.com/cholesterol.htm



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I come from a family of high cholesterol and, even as a vegetarian I've had my cholesterol too high. Oatmeal in the morning; red wine in the evening and consuming only a small amount of fat-free or low fat dairy has got me under control (well, except for that bleu cheese habit)
Nancy
However I buy 2% milk or skim milk versions of most of the dairy products that I buy, which reduces the fat content but still leaves the taste and texture that I like. 