Well also remember that when we were kids, it was unlikely that companies were putting so much chemical treatment on the clothes during shipping, so even though I sometimes wear stuff before washing it, I wouldn't do that for my kids, it kinda grosses me out!
I agree that you don't necessarily need baby detergent but I would use free and clear for sure! Baby skin is so sensitive and you just never know how sensitive it might be. My son has the worst skin sensitivity and no one else in our family does.
I basically just did the baby's laundry all by itself for about the first year. That way I could put it all together and not worry about it. After that I started mixing it in with the general population, but it just made me feel better to keep it separated at first, even though I use free and clear for everyone, which I know sounds kinda weird, but that's what i did! ;) You should also consider not using fabric softener and on anyone's clothes but certainly not the baby stuff. It can irritate skin too. In fact, as a baby my daughter was just rubbing against our clothes that had softener in it and broke out in a rash so I haven't used the stuff in 5 years!