Opening new savings account for our baby today, what type is best?

xylophone

First see http://www.hmrc.gov.uk/tdsi/children.htm and note what happens when a child turns 16 (to non JISA accounts - the JISA becomes available to the child only on turning 18) and what action is required re R85 if you require to remain Trustee after this point.

It always seems to me wiser to keep any money given by parents separate from that given by other people, at least where non-tax exempt accounts are concerned.

You could consider using an S&S JISA for longer term growth - there are various schemes available. http://www.hmrc.gov.uk/tdsi/children.htm http://www.hl.co.uk/investment-services/junior-isa

You are not confined to accounts intended solely for children - you might want to consider fixed term accounts for example. You need to find out whether the account you choose permits "re' accounts. http://moneyfacts.co.uk/compare/savings/accounts/search/ might be of interest.