APPLYING FOR CUSTODY

THIS IS A LONG POST!!!!!!
During the past week I have come to the conclusion that I want to apply for majority to full custody of my 5 year old. I am after some advice and any ideas about what I can do to make the process a lot smoother for myself and my children.
I am applying for custody of my 1st child who is 5 years old. His father and I split up when our son was 4 months old. The father has not made any real effort over the past 5 years to be a part of his sons life. I have had to ask him to come to his sons birthday each year and we used to fight black and blue over getting him to visit his son more often with myself failing and him never showing up. My sons father has not exactly been the best role model for my son anyway... He has a history of violence, he actually pinned me to the wall via my throat while I was pregnant with our son and threw a switch blade at me while I was pregnant, the arguments were horrendous. He has a history of alcohol and drug abuse and has landed himself in hospital a few times after almost over doing it. He has dealt drugs and dated a drug dealer. Each time his mother, father and siblings have said they want to visit I always let them so there is no problem with his family having access to my son. I rarely see child support, not that I really care about that, I have struggled more with getting my sons father involved. My sons father is constantly in and out of jobs every few months so is not financially capable of raising our son and his fiance flat out refuses to work simply because her back hurts often. He has moved several hours away and would not be willing to move back to where we are because his fiance would see to it that he does what she wants anyway which would make his attempt to gain joint custody a waste of time anyway. I actually tried to reason with him a few times, I said to him once that if he wanted to come and stay with his son for a week I would go stay down the road at a friends place while he stayed in my house with our son and he would have access to my bed, my fridge, my cupboards, my tv, internet, phone etc. all he had to do was get to my place... He said no. Some time ago I tried to reason again and said to him that if he got himself a little two bedroom place (he was actually in a granny flat that was one tiny room with his bed, couch, tv and kitchen in it with a little toilet in a room to the side) and could set up a room for our son I would start sending our son over there every second weekend to stay... Once again he didn't follow through. Just recently I messaged him and said 'hey, our son starts kindergarten in a week and a half, it would be nice if you could come see him start his first day in his new uniform', he flat out said said he couldn't do the small 3 hour drive because he works (I know he only works part time). I found also and it is very insulting to my son as it is, that his father would NEVER tell any of his friends or acquaintances that he even has a son, almost as if he is ashamed, I don't know.
I don't want to make out that I am this awesome mum or anything because I'm not, I'm just the average stay at home, look after my children, clean the house and get my kids ready for school kind of mum. But, in the past 5 and a half years I have put my son in daycare, preschool and is now starting kindergarten in a few days. All his immunizations are up to date. I have had 100% care of him for 5 and a half years, so since he was born. He has his own room, he has a rumpus room set up on the front enclosed verandah and I have a table set up just for him in the lounge room with his educational stuff that I have for him. I don't see how my son would be any better of if taken out of my care. His school is a 10-15 minute walk around the corner so there is no sense in uprooting him and sending him 3 hours away every time it "suited" his father to be a part of his life, my son would be better of if his father lived nearby. My son also has a 5 month old baby brother and I am COMPLETELY against separating siblings!
I am raising my son in a homey 3 bedroom house that is always clean, there is always food in the fridge, fruit on the bench and he has access to a backyard that could fit another 3 or 4 houses in it so he has an abundance of room to play. I don't want to have any of this taken away from him. I have no idea what ind of home his father lives in currently or if he is sharing with his girlfriends family or if they have another flat, I just know he can't afford a place big enough for my son to stay at.
Based on this information on our lives and what my son has what would be my chances of arranging some sort of custody agreement? I am happy if it isn't full custody as long as I have majority custody. I have no idea what I am doing here and am feeling a bit overwhelmed.