I don't even know about the first two...
First wave feminism focused on women's suffrage and equal property rights in the late 19th century and earlier 20th century.
Second wave feminism expanded the goals of feminism to address sexual freedom and combatted some of the ways in which the nuclear family restricted women's rights (such as the prevalence of marital rape). Second wave was also responsible for the unsuccessful push for the ERA.
Third wave feminism originated around the 1990's, and is what could arguably be described as "modern" feminism. It became more inclusive of transgender rights and freedom of gender identity.
To answer the question, I consider myself a feminist, as I'm supportive of equal rights for women and not under the illusion that this has already been achieved. While third wave feminism brought some needed aspects of the movement to public discussion, it was also a step backwards from second wave feminism in some respects as well, most notably the shunning of acts like pornography and sex work as anti-feminist activity.