Hi, R.--
I am going through a custody battle as I write this and it is gutwrenching. I do not know all the answers, but I will tell you what my attorney said and repeat my understanding of the law as it applies here in Oregon. There are two sorts of custody-- one is legal custody where it affects the decision making power for things like medical/activities/schooling and religion. If you are able to work with your child's spouse in decision making, life will be so much easier. The other kind of custody is physical and this is not necessarily tied with the legal custody. For example, you can have sole custody for legal decision making power and still have joint physical custody where you share physical custody of the child 50% of the time. I hope this makes sense.
In my situation, my husband was domestically violent. My attorney said she typically advocates that people share custody, but in my case where my husband has deep issues about controlling me and being vindictive, she said I should go for sole legal custody. She said that joint custody cannot be mandated through the court unless I want it. She feels certain that I will get it since I am the primary caregiver. However, my husband kept telling me that either of us could be given sole custody and that it would be in my best interest to accept joint now-- not true. This is why having a lawyer is critical. Call Legal Aid if you can as soon as possible if costs are an issue. This is such a difficult journey.
If you can work with your child's father on issues, I would suggest joint custody. As for the parenting time, this is best worked out between the two of you or the court may mandate it split down in some rather distorted ways.
Best of luck to you!