Im using presil non bio and comfort pure or supermarkets own version of tisfabric softner. This seems not to irritate my nearly 2 year old with eczema. So figure it should be okay. Last time used fairy but its quite expensive.
General advice is to use non bio but avoid a fabric softener completely as the chemicals can irritate baby's skin. I always add in an extra rinse to make sure all soap powder has gone. If you want soft and use a tumble dryer you can always use tumble dryer balls .
In terms of making sure there aren't too many chemicals left on the clothes, I always halve the powder dosage (cheaper than an extra rinse too!) - so when using the Fairy non-bio tablets I use one per wash instead of two. Works absolutely fine.