I think it depends on how bad your lipid levels are and whether you have a genetic condition that increases your lipid levels. Not everyone gets the bad side effects from statins... I think you won't know until you try them. If your lipid levels are really high, then advice to try diet first could be risky. Diet can certainly help in many cases but I don't know whether it will be enough if your levels are higher than the usual slightly elevated levels that most people offered statins seem to have.
I suggest discussing your concerns with your doctor as they may have ideas for reducing the side effects. There are probably several different types of statin - they could suggest the one with the least side effects first and you could work up to the full dose slowly. There may be drugs that can help with the side effects, enabling you to keep taking the statin you need.
For example, I take a drug for my chronic depression and anxiety that causes restless leg syndrome, so I take another drug that treats the RLS. The first drug is too important to miss out on due to a side effect.
In a perfect world we wouldn't need drugs but they can improve quality of life and extend our life, so I feel lucky there are drugs available that can help at all.