What sleep med is likely to work best depends on what kind of sleep dysfunction you have, so just because a sleep med works for one ME patient, doesn't mean it will do any good for another.
Some people have trouble initiating sleep. Sedating, relaxing, and anti-anxiety meds can work for that. Other people have trouble maintaining sleep or achieving stage 3 and 4 sleep. Medications for initiating sleep will not help with that. Trazodone is probably the most common medication to help achieve stage 3/4 sleep. There are also conditions that disrupt sleep such as periodic limb movement and sleep apnea that disrupt sleep that need to be treated differently. I'm sure there are plenty more sleep disorders many of which have different treatments. You need to know which you have in order to get the right treatment.
When I had trouble initiating sleep, Tylenol PM worked for me, but I no longer have that problem. I wouldn't consider that a good long-term, continuous treatment, but fine on a temporary or intermittent basis... for me, anyway. It is probably insufficient for more intractable sleep initiation problems.
My persistent sleep dysfunction is inability to maintain sleep. An ME/CFS specialist put me on Trazodone for that years ago and it has worked like a charm for me ever since. Without Trazodone I wake up about once an hour all night, and wake up for good (completely unrested) after 5 hours. With Trazodone I sleep about 8 hours without waking. Much better.