Potential novice dog owner.. Please help!

[NeatFreak]

We are considering getting a dog but aren't fully decided yet so won't be making any decisions yet.
I have 3 dc aged 1,6 and 10 but would rather not have a puppy. Would any/ many rescues rehome to us? I am out the house for a few hours several mornings a week but will be home the rest of the time,have a large secure garden and plenty of indoor space. Paying for insurance etc is all fine... Is there much I haven't considered? The dc will be helpful, especially the elder one who I'm confident won't get tired of a dog.
We haven't given much thought to breed but would rather not have one too big.
We did have an elderly Labrador a few years ago after a relative passed away but she just slept most of the day and had a couple of walks a day so was no trouble at all.
Any tips or advice would be much appreciated. I don't know much about socialising, training Etc but would explore that and anything else!

Find all your smaller local rescues, they often are happy to rehome to a home with young children. If you want a dog that is really assessed it's best to get one that has been fostered rather than in kennels. My first rescue (from a large experienced rescue) was assessed in kennels and they got it utterly wrong. I wouldn't risk a dog that isn't properly assessed with such young children.

Crate training quite soon is a good idea - most can be crate trained. Separation anxiety is quite an issue with rescue dogs due to them being abandoned once or maybe more and they take a good long while to settle properly.

Dog training classes are a good idea for all dogs of whatever age (they train the owners as much as the dog).

Btw, your 10 year old will get tired of a dog when it's raining every day and the dog still has to go out

Agree that smaller local rescues less likely to have blanket no kids policies, one I volunteer with assesses every home individually, and they do have histories for some dogs that are handed over, so can tell you if previously housed with kids happily. Avoid the littler dogs, tend to be more snappy! Staffies are fabulous family dogs

Thanks for the replies and apologies for not replying sooner- I've spent most of the past week doing doggy research
Completely against what I thought I'd decide, I think I'm decided on a lurcher/ greyhound type dog. We are going away for a week at Christmas then a long weekend in February so it wouldn't be fair to do anything any time soon but I think that is our decision...
Any tips, dos and donts would be much appreciated. I've done loads and loads of research but there is probably still a wealth of information I've yet to discover!