I would go for a local authority in the first instance if they are remotely suitable.
The reason is that (sorry if this comes across selfish, but it's the system in our area) the local authorities actually have the children to place, from their children's services teams. They will try to match with their own pool of approved adopters first before passing children to the wider adoption register (which includes adopters from private agencies). Essentially that means that the younger, easier to place children, get matched with the LA's approved adopters.
Only harder to place children such as older ones, difficult circumstances, bigger sibling groups, special needs, unusual ethnic criteria, tend to make it onto Children Who Wait etc. Of course these children need families too, but if you feel that it's beyond you to manage those kind of issues, you may be better with a LA even if you find the "service" a bit slower.
I say this because I know a couple who got approved by a private agency, they would make superb parents and are younger than many adopters, but they will be lucky to be considered for a baby or toddler because of that system, they are reliant on the publications.
That's a bit of background and that's why as Kristina says, ask the agency for the age breakdown of the children they have available at the moment or placed last year to give you an idea. I was staggered to find out that our LA actually placed a lot of under-twos, when people are always being told there are no white babies available for adoption.
Other questions you could ask are - what post adoption support is in place, are you likely to get an adoption allowance, how long should you expect to get approved (about a year after prep course), and do you fit the profile of adopters they are looking for. If you are prepared to take a sibling group of 2, you will be much more interesting to them!