My 19 year old sister has two kids. One is 3 and one has just turned 1. Both have different dads. She doesn't have a GED, and she doesn't work. She is currently living with my mom. The father of the little girl who is 1 has recently been put in prison for up to 18years (still waiting sentencing). She married the little girls father after he was put in jail. It is suspected they were married so he wouldn't have to pay child support. My mom is working two jobs trying to support my sister and her kids. My sister currently has a warrant out for her arrest for not showing up to court. I want to adopt my niece and save her from a disastrous childhood she is destined to have if not removed from this situation. I currently live with my boyfriend, I have for the last two years. He has a very respectable, well paying job, as do I and we want to bring her into our home and provide the best life for her possible. We plan on getting married at some point and would do so sooner if it would help the situation. I am looking for advice and guidance on how to begin. I don't want to cause too much trouble for my nephew if avoidable.

Getting married would help make you better candidate as far as Children's protective services goes if and when they investigate if you would be a good placement for your niece.
You really can't just try and adopt your niece out from under your sister you can offer to take her in and be a guardian until she is able to care for her herself. You can ask if her AND her husband would be willing to give her up for adoption. If Children's Services becomes involved you can request the children be turned over to you as their guardian, foster parents, adoptive parents.
Her marrying the father would not stop him from paying child support. I know father's who live with the child and still pay support. He is responsible simply because he is the father.
I would say start by talking to your sister and parents about guardianship and take it from there.