There's enormous variations (as you've already discovered) between rescues - it's a completely unregulated sector and anyone can set themselves up as a rescue.
Larger, national rescues such as Dogs Trust, Blue Cross will have minimum standards and DT definitely have post adoption support available from their behavioural team. Larger independents and the big chains will be members of the ACDH - this is a useful benchmark as it shows they are committed to benchmarking, continuing learning and at least learning about best practice.
What you'll tend to find is that the bigger rescues will have slightly more inflexible rules and often a slightly less personal service - smaller rescues will often be willing to be more flexible and treat each adoption as a one off.
If you have a particular breed in mind, it's worth getting to know the specific breed rescues - depending on the rarity of the dog, they might be local or regional or even national. Start following them on FB, and swot up on their adoption processes. Sometimes you can get homechecked before a suitable dog comes up. If it's a local rescue, then I'd strongly advise getting to know them and possibly doing things like attending their events, offering to walk kennel dogs, volunteer at an event etc. All this will give you a much better idea of how the rescue runs and you'll get to know their dogs too.
As a minimum, the rescue should do a thorough homecheck before you adopt - expect detailed questions about your family circumstances, a good look at your garden and your expectations of pet ownership. Many rescues WILL adopt to people who work but they will want to see evidence that you can afford doggy day care or a dog walker, for instance and that you've thought about your arrangements.
They should also be able/willing to talk you through the adoption process and explain how the adoption will be supported on an ongoing basis.
If you are interested in a particular dog, the gold standard is for the dog to have been in a foster home (this is particularly important if you have DC, and the foster home has DC). If this is the case, the dog will have been assessed very thoroughly.
The rescue will be able to tell you something about your dog's history (but don't be surprised if this is sometimes a bit scanty) and the dog should have had a thorough health assessment so you should be made aware of any known issues. They should be able to give you a behavioural assessment - common questions would be if the dog is cat friendly, child friendly and dog friendly. Other useful things to know are whether they travel well, can be left alone or prefer to be with other dogs, what if any training they've had, what they eat, any habits or preferences etc.
Most rescues insist on their dogs being spayed/neutered before adoption (unless a puppy in which case they'll expect you to arrange this once the dog is older), the dog will be chipped, and have had flea/worm/tick treatment plus usual vaccinations. They will usually insist the dog is kept in the house, not in an outside kennel, and will also insist the dog is a pet and is not to go to a working home. They will ask about your plans for the dog e.g.activities or sports - for some breeds this will be very important so be clear about this and the time commitment involved if you are going for something like a border collie.
Hope this helps!