Always share your 'info answers' as many others may have the same question.
You did get the 'main' three down but every state is different and custody can be assigned in a manner beyond the 3 options...such as joint legal, sole physical...primary & secondary w/ joint physical...or P & S w/ joint legal, sole physical,etc,etc....joint physical w/ a primary,secondary & sole legal...it really just becomes ridiculous.
If you read your state laws on custody or state where your case is handled...sometimes that is better than having a lawyer....and if you can keep up with all the rules, exceptions,changes,etc,etc...then you really should consider a career in family law,lol! Don't feel bad if you feel overwhelmed looking for 'the right' answers, just join the club. Always do your own research though...here you can get 'great' experiance advice, but don't assume it is concrete for sure information. Every state,case,lawyer and judge are different....there are few absolutes in custody. Good luck, knowledge is power....