There was a great thread for a similar question a little bit ago. I'm sure there is much more to add but It should give you a good start.

Some highlights.

Suffrage led to a huge boost in voter turnout but how much is in dispute.

30 states already had women's suffrage before universal women's suffrage.

We are unsure of the exact split of women voters between political parties but it was a fairly even distribution.

Suffrage did not likely change the outcome of the 1920 election of Harding.

A follow up question, if 30 states already allowed women voting, were these women allowed to vote in federal elections?