Yes- this is a much more complicated question than it would seem. The "types" of Judaism are more like a bunch of siblings. They don't always agree on everything, but we certainly don't see each other as seperate.
The idea of "egalitarianism" is also kind of trickey... It might *appear* that in orthodoxy women do not have the same status as men, but in many ways, it is... different. So, don't cross it off entirely without even thinking about it. If you are converting to Judaism, you will find that there is a lot of connection accross "divisions", so if you are truly uncomfortable with the whole idea or the people in it, this will be a sticking point. Reform Jews might disagree with Orthoox Jews about certain issues, but they don't reject them or deny them or even hold hard feelings. Just disagree. And disagreement among Jews (within the family) is expected and OK with everyone. We argue with eachother all the time! A branch might feel more comfortable to you than others, but, you're still going to be sitting at the "dinner table with your siblings (of other branches)" at some point, so if you are so "against" a branch so much that this is not possible, it will be... hard.
A conversion to orthodoxy would drastically change your life (there are family purity expectations, expectations regarding food, prayer, etc.). A conversion to reform or conservative Judaism would also be life changing, but... not in the same way. I think most converts tend to be drawn more to reform and conservative branches. But, people do convert to orthodoxy.
Only orthodox conversions are recognized by Israel. Mostly. Some orthodox conversions aren't. Conversions that Israel would recognize are very specific and if you think you will make aaliyah (moving to Israel), you should discuss that with a rabbi. Otherwise... what the Israelis think about your conversion generally won't have a huge impact on your life. But, then again, the American orthodox won't recognize a conservative or reform conversion either. But your "branch" will accept you. At some point you have to decide if it is about what is in your heart or about who likes your papers.
As for circ, the official party line is- none of the major branches of Judaism will excuse a Jew from being circ'd. But, you need to talk to a rabbi regarding an uncirc'd child converting. Personally, I could not imagine approaching that with a child before they become an adult and can consent. Jewish babies... well... Adults converting... but kids? Hmmm...
Not all rabbis will refuse to discuss conversion. However, Jews take it very seriously (and with a bit of skepticism). It requires a lot of personal conviction and changing the way you live and how others see you. Jews know that being a Jew can be hard and a convert to Judaism is even harder, So, don't be (too) put off if they don't fall all over themselves to drag you to the mikveh

. Be sincere. Go from there.
I would recommend "wading" into the pool... Reform Judiasm most often makes the most "sense" to non-Jews and does not "require" adherence to many of the "rules" that other branches do (maternal lineage, kosher, etc.). Then, move around until you find what is comfortable. A reform rabbi will absolutely have no issue (and will recommend) you talking to other rabbis of other branches. There is no animosity that way. We really are all one family.