The first step in considering conversion is to learn about Judaism and Jewish history on your own, so you can choose, first, whether you want to be a Jew (not an easy choice) and also what kind of Judaism you would want to pursue, because there are many options. This site is a great place to start, though it often only presents an "Orthodox" perspective. I'd suggest that you go to a synagogue and ask if you can use their library. A public library is great too but synagogues often have a better selection. Some great books to begin learning about Judaism are the "master histories" such as Heinrich Graetz's History of the Jews (it is in so many ways out of date as it was written in the 19th century but it gives a good overview) and the Encyclopedia Judaica which has great articles on many aspects of Judaism such as the Kabbalah, issues relating to Biblical criticism, etc.
Just to be clear, you do not need to convert with an Orthodox rabbi to become a "real" Jew. You have a choice of what kind of Jew you want to become, just like someone who was born to a Jewish family has a choice of how he or she wants to practice, but they are still Jewish.
Now, there are some "legal" consequences to a non-Orthodox conversion, as discussed in detail in this questionthis question's answers. That is to say, the Orthodox community may not consider you Jewish. But even if you convert with a non-Orthodox rabbi, you will still be able to immigrate to Israel as a Jew under the law of return, which recognizes non-Orthodox conversions.