I entered the anime scene my junior year in college after seeing Fushigi Yugi and Yu Gi Oh. Then I saw Rurouni Kenshin, fell head over heels in love with the show, and never looked back. When I married, I quickly hooked my husband on anime and now we rent it through Netflix regularly. Renting has saved us from a lot of buying mistakes over the years, enabling us to buy only the shows that we just cannot keep out of our minds and want to watch over and over.
My only advice to anyone getting started in anime is to read reviews of content in a show before renting or buying. I have always done this so I have never seen anything all that upsetting. You have to keep in mind that anime comes in every genre you can think of including horror and lesbian. Plus, there are no ratings. Therefore, any show just might contain things you just do not want to see, so make sure to check ahead of time from a reliable source.