Well i use j&j products. i have had no problem with them, moisturers , bath wash.

Bongela i keep it has been wonderful during teething (but you will have a little while until that anyhow).

I keep talc (you find they dont contain aluminium now) and use it during summer to prevent heat rash and excess sweating in bubs (esp if you have no air con or in a hot area).

Panadol and nurofen i have - but note the use by date - esp if you are keeping for when bub is older - you may want to buy later down the track.

I got by for 2 years without a thermometer. i just felt bub to know they have a temp - otherwise a $10 one will do the trick.

Some sorbolene cream for cradle cap.

mmmmmm

i also use zinc cream for nappy rash or bepanthen.
i have paw paw too (simmons) but find it is ok for mild rash but doesnt do the trick for dreadful rash.

HTH