What a great assignment! This an amendment ripe for discussion, and how you go about addressing it is a question of what your focus is going to be. I see you have listed your question under the category of "Law and Politics," but that still gives you a great deal of latitude. Let's go over a few ways to frame your paper, which is what a thesis statement is meant to do.
Your paper could focus on the road to the amendment, what it took and how long it took to achieve this equality for women. A thesis statement for that focus could look like this:
Some key reformers, picketing and civil disobedience, and lobbying over more than a hundred years resulted in the passing of the Nineteenth Amendment.
This would give your paper a structure, with one section on each of these facets of the movement.
Another way to frame the paper might be comparative. You might have done some research on when the United States gave women the vote in comparison to other countries, and it would be interesting to analyze the differences amongst those countries, I think. I don't know if we were ahead or behind or why either would be the case, but you could write a thesis statement stating the differences and the points that led to these differences, politically, culturally, or economically, for example.
It might also be interesting to analyze the results of the Nineteenth Amendment, for example, how many women actually registered to vote initially, or even up until the present, or how many females have been elected since then. It does not appear to me that giving women the vote has resulted in anywhere near equal representation of women in government, and that is something well worthy of critical analysis. I don't know what your research will yield on this, but a thesis statement might very well make the argument that the Nineteenth Amendment as not done womankind all that much good, and then add the points that support that contention.
I wonder to what degree the passing of the Nineteenth Amendment contributed to the gaining of equal rights for women generally, whether this was a big breakthrough or it slowed progress down because everyone thought the battle was now over. You could examine all of this within the context of women's rights generally, stating that the amendment was a big boost or caused the movement to stagnate, and why.
You could also look at the amendment within the context of the movement toward equality before and around the same time. You could examine what other rights women already had, for example, the right to own property or hold money in their own name? How did the amendment fit into the overall picture? A thesis statement for this would involve a main idea about how the amendment fit into the overall scheme of things at the time.
Another aspect of this topic might be to ask to what degree equality for African-Americans informed and influenced the battle for the vote for women. Was there a relationship? Did women use the African-American playbook to formulate their strategies? I have a feeling they did, and this could be an assertion you could make and support in a thesis statement.
Since I don't know exactly what research you have done or what kind of course the paper is for, I have tried to provide a variety of ideas, in terms of law, politics, history, and feminism. I hope one of these works for you, or that it at least triggers some further ideas that you can use. Good luck!