I forget which kind of migraine/headache it is, but you know the throbbing ones? Where it feels like you can painfully sense every beat of your heart through a narrow strip on your head somewhere?
Cannabis has only ever made those throbbing headaches worse for me. It helps relieve pretty much every other headache I've ever smoked during, from sinus to tension to those entire-side-of-your-head, can't-look-into-the-light-or-hear-
ANYTHING-above-3-decibels-without-cringing migraines, but when they throb I've personally noticed that smoking weed only makes me more aware of that kind of pain/symptom. Just a fair warning on that one.
As far as suggestions... I would recommend indica-dominants, preferably the ones that people label as good for killing pain. Leafly's a good, but not infallible, site to start your search:
https://www.leafly.com/explore#/explore/symptoms-headaches,pain
Strains with more reviews? I've found those to be much more trustworthy and overall accurate (in the reviews) than the ones on that site that only have a few people giving their opinion. Call me cynical, but I like to have a diverse pool of information to make a more informed decision on pretty much anything.
The reason I, personally, would stay away from the typically "heady" high of most sativas is specifically because they give heady highs and they tend to be, again in my experience, more psychedelic than the indicas. They could very well provide relief, but when I have a headache I just want to lay down and forget about/sleep through it, and with sativas it's always seemed like there was a higher chance of that heady high making my headache worse. I don't have any experience to back that up as I'm generally an indica man myself, it's just been a general assumption I've operated under when it comes to smoking for legitimate medical relief.