I'm really not trying to be antagonistic, so I hope it doesn't seem that way- just think it'd be healthy to consider the other side 
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I wouldn't consider a rescue in my circumstances, I've known 3 separate cases of rescues that have gone horribly wrong
I am being perfectly honest when I say that I personally know of many more than three breeder-sourced dogs that have developed or caused huge problems. I do also know of a couple of rescue dogs that haven't worked out as hoped- but honestly, fewer than the bred dogs. Possibly because the process tends to be more thought out and more well-matched to the individual dog's traits (rather than relying on breed or bloodline) than with sourcing from a breeder, but that then leads on to your second point...
not all rescues have experienced staff who are good at matching dogs and it's just not a risk I would take. I think buying a puppy from a good breeder who knows their dogs...
I completely agree that not all rescues do a brilliant job, but the same can be said (realistically, more so) of breeders as a whole. It is no more effort to source a reputable rescue than a reputable breeder so I'm a little confused by this reasoning.
buying a puppy from a good breeder who knows their dogs and their dogs temperaments going back many generations, ie a lot of breeders have grandparents , great grandparents, siblings and know their dogs temperaments very well is in my personal opinion a much safer bet.
The family history of the dogs is no guarantee of the puppy's temperament. A good breeder will breed for temperament, of course, but it is always a big gamble regardless in a puppy. Some would argue that actually highly-bred dogs are more likely to be highly strung or develop neurological defects due to smaller gene pool- though that's a whole other topic. Adult dogs are by their very nature less unpredictable in terms of temperament as there is a little more evidence to go by- though of course you still have to consider that temperament is a plastic changeable trait that varies in different environments.
You can expect certain traits and thus suitability in certain breeds.
Honestly, I do think may be slightly true on average (so if you were to get 100 dogs then they might on average tend to a particular trait), but massively overemphasised. If you look at how people describe any particular breed, and look at the words that follow, you could literally change the breed name to anything and still believe it. Except for things like hairy, large etc of course! 
to have fun, to socialise to have days out at the odd show with my dog
Sorry, that question wasn't meant to sound sneery- just curious. Have you considered activities such as agility as well? Might fit more with what you'd like to get out of it. The show world is quite variable and can be intense- sometimes great, but I know a few people who have quit as it just got bitchy and overly serious even at low levels. Perhaps depends on area.
Just some food for thought
Anyway, in response to the original question about the flat, it really does depend. Generally I'd advise strongly against. I know a couple of people who successfully have dogs in flats- both large spacious flats (no cats either), both child-free with one person home to take dog out constantly. In a smaller flat with children and cats I can't really imagine that being as easy to pull off. (I'd also worry about the cats struggling to get space away from everyone else potentially).