Hi and welcome Hilary 
In terms of agencies, I would recommend calling and having a chat with your possible agencies - pretty sure you can do a post code search online at the government's First4Adoption site - and then going with the best of those. The difference with an LA (council) is that they are the ones who take the children into care and so they are the ones who have waiting children with them. Generally, a council will look to their own adopters first, then to a specified set of other nearby councils and voluntary agencies, and then after that they look further afield (geographically). It's impossible to generalise, but some VA's specialise in placing hard-to-place children, so older kids, sibling groups, children from ethnic minorities and children with disabilities or other significant needs. Yet sometimes people go with VA's and adopt young single children, it totally depends on the area of the country you live in and the individual agency. So you would be best to specifically ask the individual VA's about the type of children they usually have placed with their adopters, and if that fits with what you would like, then great. Again, all agencies are different, but some VA's have better post adoption support than any other agency, you might find adopters to give reviews of agencies in your area.
But ultimately, unless you are lucky, not all agencies near you will need what you have to offer at the moment. Some will be less enthusiastic about you than others. All work differently. So it's best to have several discussions and then make a decision. You can attend multiple open evenings with agencies as well as phone them.
You do specify an age range (at first they just want your general thoughts, you aren't expected to know for sure until later in the process), and they ask people so they can prioritise those applications from those people they think they can match with their waiting children quicker. There are less children waiting for adoption now than there were 2 years ago, and no one knows for sure what will change in the next year, but if you want to adopt a single child under the age of 3 who doesn't have significant needs, you will need to understand that you may have a wait after you are approved. How long does it take to find a child, is like asking how long is a piece of string but some people are waiting over 12 months to be matched right now, or even 18 months+ in some counties. Others are lucky to be matched in under 6. But I think the mental preparation for a wait is key.
However, you have to go with the age range you feel comfortable with. 0-2 years is usually the youngest age range people ask for, and they are usually bringing home children aged 9-23 months within that age range. A few people ask for 0-12 months but right now there really are few children within that age range. Under 6 months IMHO is not realistic unless you are interested in concurrent planning, which is when you foster a baby who is likely but NOT certainly going to be adopted. If the birth parents don't manage to turn things around and none of the other family are suitable, you then adopt the baby. So it's quite different from going the adoption-only route.
In adoption terms any child aged 23 months of younger is a baby, so 0-23 months is a realistic age range IMHO, as long as you are happy to possibly wait a while.
That's the younger end obviously, you might personally want to adopt a child older than that, there are few children older than 8-9 available, but any age from 4-9 is also realistic.