I started off with Omo Sensitive and always washed all our clothes in together. I was too busy to sort out the baby's clothes to do a separate wash for him (not to mention all the vomiting and pooing that was going on, I needed to stay on top of it).

He started getting eczema at only 6 weeks of age so I stuck with the Omo Sensitive and eliminated fabric softener. When the eczema calmed down at about 6 months I tried to go back to "normal" detergent (eg Radiant, Omo, Drive) but DS would immediately get eczema flare ups that would calm down as soon as I went back to Omo Sensitive.

I have since found that Bio Zet (plain green box) also doesn't aggravate his skin so I use that now (often on special - Omo Sensitive is NEVER on special - and it has a fragrance, I really missed having nice smelling washing). I'm pregnant with Number Two now and will stick with the Bio Zet - I figure DS is a good barometer!

Long way of saying - yes, I would use a detergent for sensitive skin for the first few months. And no fabric softener, the residue stays on the clothes. You will soon figure out how sensitive your baby's skin is. Lucky you if not, it really is a pain!