I pretty much agree with everyone! Although I would say that it is my understanding that it is not the job of a local authority to find you a child. They assess you because they want you to adopt one of their children. They probably only take you on if they think that this will be the case. So if lots of people were asking for babies and they rarely had babies in their area etc they would probably stop 'recruiting' potential adopters looking for babies.
It is a subtle difference but it is my understanding that local or county authorities are looking for couples or individuals or families for children, not the other way around, so they may not go out of their may to find you a child if they do not have a child they think you could parent.
Having said this....
Some authorities will work in collaboration with other areas of the country (probably close by) and if a child from a neighbouring country is placed with one of their adopters it may be good for them so they may tell you about children in the other areas or they (in the case of our county authority) will tell you about some sort of exchange event where you can go and hear about children in all the counties represented.
Usually the information times are called an exchange day or information day and are where just information and social workers (and some foster carers) are present. The other type of event is where the children (usually harder to place children) are present and also information, social workers and usually the foster carers. These are at a fun event usually called an 'activity day'.
Also, if the country really cannot match you or if you have been approved for three months or more you can apply to go to an exchange event run by an organisation like Adoption UK.
www.adoptionregister.org.uk/adopters/exchange-days
Or an activity event organised by BAAF
www.baaf.org.uk/ourwork/activitydays
As far as voluntary agencies go I have known a few people to use them and it was always because of special features such as a Christian family who used the Catholic one or a military family who used the military one. And I know if you adopt from overseas you can go through PACT.
I personally cannot see what benefit that voluntary agencies bring as they do not have any children to place but I am sure that they do suit some people.
We just went with our local county and have been very happy and have had excellent post adoption support (our little boy has been here about 9 months and was three when he came).
But in your shoes I might look at local authority or county ones, more than one, and voluntary agencies and be asking all your prospective agencies the same questions. Then I would be collating the answers then go with the one which either answers the questions the best for you or your gut feeling or a combination of those or other factors!
The questions I would ask would be about whether they would be interested in you as adopters, the kind of children they usually place with adopters, the training and preparation they offer, times scales and the kind of post adoption support they can offer. In some ways although I have listed them like this I feel the post adoption support question could be the most important one. I would be looking for concrete answers and not a vague 'we will support you'!
Good luck.