I think you'll need to partition the garden to keep the chickens safe and not too stressed.
You need to think about what size you want, how much shedding you can live with and your opinion on drool. Do not get either a cav or a flat faced breed without reading up thoroughly on the health issues and deciding if you can live with a dog that might prove to have difficult issues (health tested parents reduces but does not necessarily remove the risk. Be aware that insurance for these breeds is likely to be expensive.
All puppies chew when they are teething, so you'll need to puppy proof for that stage, and teach the dog, over time, what s/he can have
If you get a puppy, the cat will probably do the 'cat training' for you, as long as s/he is reasonably feisty. Cats need a place where they can escape from the dog if they want to - maybe allow the cat upstairs but not the dog?
One of the smaller, friendlier terriers might be suitable - both the Norwich and the Norfolk are excellent family dogs (small, robust, can go all day but won't mind the odd day of short walks only, easy coat care, usually very good natured) but one is a vulnerable native breed and the other at-watch, so hard to come by (plus side is that they tend to come only from breed enthusiasts, rather than larger-scale commercial breeders)
Also worth considering Border or Cairns terriers, which are also at the friendlier end of the terrier scale