LEM prepares for a flaming - I dont see why you can't have a dog to be honest. PRoviding of course you are prepared for the work involved in training and looking after it. I agree that you shouldt leave the dog all day but there are solutions. Dog walkers could take your dog out for you on the days you were working, so it would only be alone for a max of four hours in a row, unless of course you work mad hours. Obviously this depends on expense and finding someone you trust. My parents used to walk my dog for me. So long as you research the breeds, as certain breeds do suffer from separation anxiety more so than others. You could give Battersea dogs home a call, they would be happy to help - i am sure their rehome policy is that they will rehome a suitable dog to an owner who works, providing some provision is made for the dog during the day. I would probably not go for a rescue dog if you have young children and certainly battersea wont consider you but i am sure they would give loads of advice.
I think a childs life is enhanced in so many ways by having a dog in it. If you can find a way around getting someone to walk or let him out for a piddle when you are out, and obviously you might have to take some time off while you settle him, it will be fine, honestly.
Cage pets are OK, but i would rather see a dog on its own for a few hours a day than a rabbit stuck in a cage 24/7. TBH with the best intentions in the world, this is what happens to most pet rabbits and it breaks my heart. Hamsters, imo - give nothing back, people might disagree but i just dont think they make good pets. Rats on the other hand, if you really can't have a dog, and dont fancy a cat then a rat makes a great pet (better than cats imo, but im weird) - they are intelligent, responsive and easy to handle.