The first thing I would do is check what my TSH and other thyroid bloods actually ARE... if they are in **optimal** ranges, (and i would guess they are NOT!) then the issue of thinking about Statins MIGHT need to be considered, but No.1 is get thyroid issues controlled first.
Once you know where you stand there, then there are plenty of other ways of reducing cholesterol if you actually DO need to, before considering statins... do some research on the MANY things you can do - eg. take Plant sterols (Beta sitosterol) fish oil, oats (watch carbs levels,, too many carbs are not good, keep to low glycaemic load ones), cinnamon, nuts esp walnuts and almonds), replace fats with olive oil, cut coffee intake, try green tea, exercise where possible, increase dietary fibre, don't smoke, take niacin (but beware, there can be problems with this so researc it!), possibly supplemtn magnesium.
There is a lot of info out there, so don't just take what I say (or anyone else) blindly, but many of these are known to have effect, so do your homework, there is a lot to do!
When or if they don't work, then think about statins, but beware, they rob you of Coenzyme Q10 and other substances such as selenium so it might be wise to supplement too.