My experience is US-based so quite different.
DD, DS, DD's boyfriend and I have all been diagnosed with ADHD (we have a wide range of co-morbid conditions between us too).
We've all been diagnosed by either psychologists or psychiatrists, within maybe 3 months of first mentioning it to our GPs or schools. DD's boyfriend didn't go via a GP - he just self-referred to a psychologist.
The process varied but we had to fill in questionnaires, have school fill in questionnaires, take assessments, etc.
We've all been prescribed medication as soon as we were diagnosed, and have been able to try different medications easily. DS and I got our prescriptions from our GPs, DD from her psychiatrist, and her boyfriend from his psychologist.
We've been offered referrals to psychologist and therapists as seemed appropriate.
All of this has meant that we've been able to get the accommodations we've needed at school, university and work pretty easily too.
I think the cost of diagnosing us all and providing medication and accommodations has resulted in far greater savings along the way in terms of not failing at school/college/work, becoming happier more productive citizens, avoiding those traps that people with ADHD are more liable to fall into such as drug-taking, speeding, etc.
None of us has particularly wonderful health insurance. Three of us are on insurance policies that do not cover brand name medications, so we are on methylphenidate ER rather than Concerta, atomoxetine rather than Strattera, etc.
I've been happy with what we've been offered and how we've been cared for. Providers of mental health services are not unlimited here, but they're more available than in the UK IME (I actually used to be a counsellor in the UK).