I have taken so many different migraine preventatives that it isn't even funny. Esp since I had them for 20 years before anyone told me that there were medications that could prevent/control them! I had been treated for them for at least 15 of those years!!!
Anyway, most people start with a beta blocker. These are blood pressure medications so if you have low blood pressure this may not be an option for you. They will make you tired for a while, but it goes away. Propranolol was long considered to be the most effective migraine prevention medication available, according to four of the neuros who treated me over the years and some research I did way back when. There are a TON of beta blockers and you may tolerate one more than another. One really great thing about beta blockers is that they are dirt cheap. Propranolol used to be one of the more expensive ones, but my dad took atenolol for years and the retail price of it was about $2 for a month worth.
Calcium channel blockers like verapimil are the next step that the docs took me through in trying to control my migraines. They are also heart medications. I didn't take it long because it didn't help and upset my stomach.
Tricyclic antidepressants like doxepin, amitryptilene, etc are often used. these knocked me out so I could only take them at night. I have an aunt who took amitryptilene for years and it mostly stopped her migraines. It is also good if you have chronic pain as it is helpful with those also. many people got upset when docs would rx these for migraines, thinking the docs were telling them that the migraines were not real, that they were really just depressed. It wasn't true because the dose that treats anxiety etc... is far higher than the dose used for migraine prevention, chronic pain, fibromyalgia, etc.... Very small doses are often all that is needed for migraine control. At one point I used doxepin liquid and took between .5 and 1.2 ml per night - the size dropper used for infant tylenol was what I used to measure the medication. It changed based on how the fibro was doing that day because it helped iwth both.
The final type of medication that I am familiar with is antiseizure medications. depakote, tegretol, neurontin, lyrica are all helpful. I refuse to try depakote because I have seen how it just balloons weight in many people. i struggle enough with that and it also has a lot of other serious side effects. I took lyrica for years with excellent results. not so much for the fibro and pain, but for the migraines it was one of the best. Topamax is in this category also.
I hope this helps. I did not list all the medications in any one class of medications. just soem that I am aware of. You may want to search for names of medications in those classes. Check to see which of those are on the Walmart cheap rx list and how much the ones that are not on the list cost. NO sense starting off with the most expensive medications unless it is necessary, Know what I mean??