Mixing baking soda and vinegar won't work. One is an acid and one is a base, they just cancel each other out. And oxyclean just throws another oxidizer into the mix, which will work against any vinegar or baking soda left. Just use the vinegar, with detergent if needed in the wash, and just vinegar instead of fabric softener in the rinse.
I can't say anything about best press. I don't use anything with added fragrance.