I've just read advice in a 'How to Write for Children' book that as a would-be-author it's best to approach publishers first because agents generally don't want to take on someone without a published book or two under their belt. On the other hand many publishers don't accept unsolicited manuscripts. Does anyone on this site have actual experience to draw on regarding this?
That's terrible advice.....or at least very poorly phrased. Most publishers will not even look at submissions that do not come via an agent. Very occasionally, mainstream publishing houses open their doors (or inboxes) for a limited period of time to anyone who wants to submit. "Vanity" publishers are different, of course; they don't require writers to have an agent.
Of course agents take on previously published writers but these writers tend to be people whose relationship with another agent has ended for some reason or other or people who have self-published successfully (ie high sales and good reviews). However most writers taken on by agents are previously unpublished. Yes, it can help to have some sort of track record - competitions won, short stories placed, a positive social media presence - but these are not pre-requisites, and different agents attach differing levels of importance to them anyway.
So, in summary: approach agents first unless (1) a particular publisher is actually soliciting submissions from un-agented writers or (2) you want to go down the self-publishing route and are comfortable with the knowledge that limited or only moderate success might further hamper your chances of finding an agent.
Sorry if all that sounds bossy but, without going into detail, I am speaking from experience. Check out a few agents' websites. Many of them will say they are seeking/enjoy working with debut authors. They mean it! It's just that there are an awful lot of would-be debut authors chasing them.....;-)
No, I'm sorry I don't, I SO wish I did.