Doing the cable cast on, I think you are correct about needing to put the needle with the yarn attached to it in your right hand before joining. So far so good.
Some people knit with the knit side of the stockinette on the inside, I don't, and for the life of me I can never get a handle on what causes folks to get started this way. It is not your cast on that causes it though.
There is a free video on how to work in the round here under the down menu under the "free videos" tab at the top of the page. Try watching that and see if it straightens you out. It is under either "advanced techniques" or "tips", not sure which.
Working inside out will work with no problems in a lot of cases. I know sometimes it requires you to make some adjustments in directions further on. But some folks actually prefer to work this way anyhow and learn to make the adjustments. Your choice.