The first thing I recommend is don't jump at the first puppy you see. This dog will be with you for possibly the next 15 years and you should research thoroughly before deciding on a breed that suits your lifestyle. Remember that there is a good chance that the child will get fed up with the dog once she realises what is involved, eg, grooming (toy breeds usually need alot of grooming), walking , feeding, biting, peeing all over the place, so you will probably be left to do all the unpleasant duties 
.
If you are looking to get a pedigree dog please make sure you go to a responsible breeder that does all the necessary genetic tests for that breed eg, hipscoring, eye-testing, DNA testing - ask to see proof of the results. Buying a dog from un-health tested parents often leads to high vet bills and alot of heartache for the owners. Remember a once over by a vet is NOT good enough.
As for finding out about different breeds, check out the Kennel Club Website www.the-kennel-club.org.uk , click on Discover Dogs and then Breeds and then you can view all the breed standards of over 200 breeds. If you are looking for a small dog your first port of call should be the toy section. I would only ever buy a dog from a Kennel Club registered litter and from a breeder affiliated to the revelant Breed Club. Although this will not ensure that the pups are healthy, it does guarantee that the breeder has conformed to the rule of the KC, eg, only breeds from a bitch over the age of 1 year and under 8 years. I should also stress, please do not buy from anyone who breeds more than 2 different breeds (3 at a push, if they are well known responsible breeders in each breed) or anyone who has more than one litter(2 at a push) at the same time, as IMO they are more than likely Puppy Farmers or puppy dealers, breeding from unhealthy parents and raising poorly socialised and sickly pups. I would also never buy a pup registered with any other dog registery scheme - In my opinion the Kennel Club registery is only one worth the paper it's written on.
Once you have decided on the breed you like, contact the relevant Breed Club and ask for a list of responsible breeders. When you go to visit the breeder and the litter you should see the pups with the mother. Good breeders will ask you lots of questions about your homelife and family - some may even want to visit you to check out the house. A good breeder will be there for you through a dogs life and will be a valuable resource for any queries you have.
As for price, it all depends on what breed you decide to go for - most toy breeds sell for between £400 - £800.
If you are not that bothered if the dog is a pedigree or not, then check out your local Recsue Centre or have a look here www.dogpages.org.uk. There are always small dogs looking for new loving homes, just make sure the rescue know your requirements.
Hope that helps
Never buy a puppy from a pet shop or puppy farm.