High density lipoproteins (HDL) are generally protective, so higher is better. Low density lipoproteins (LDL) are generally atherogenic, so lower is better. High triglycerides have some atherogenic potential and, if levels are very high, can cause pancreatitis, a life threatening illness. Improving your lipid profile will result in a lower chance of you developing problems in the future.
Statins are the cornerstone of proven therapy to improve outcomes. Statins lower LDL a lot, raise HDL a little, and modestly lowers triglycerides. There are a few people who cannot tolerate any of the statins, but most people can find a statin they can tolerate without side effects. There are many different statins available in the US, and if your statin reaction was not life threatening, you should probable try each one of the statins before concluding that you cannot take a statin. Also, one of the statins, rosuvastatin (Crestor) is probably helpful even if its only taken two or three times per week.
Depending on your HDL and triglyceride levels after you are on a statin, you might add niacin, fish oil (in prescription drug form called Lovaza), or a fibrate. These raise HDL and lower triglycerides. If you are one of the few who cannot tolerate any of the statins, then ezetimibe (Zetia) or bile acid sequestrants can be used to lower LDL, with niacin or fibrates added to improve HDL and triglycerides. High dose niacin, fish oil, or a fibrate can be used alone if the LDL is not too high
Let us not forget what we can do to improve ourselves, without medicines. A low-sugar, low-simple-carbohydrate diet with regular aerobic and muscle-building exercise, can dramatically lower triglycerides, improve HDL and LDL numbers, improve insulin resistance, as well as improve our general health and sense of well being.