I think a lot of this will be based on what kind of insurance you have and where you live, as well as if you are established, and oddly enough what medications you are on.
A lot of doctors only take certain insurances. So if you have private insurance and the doctor only takes private insurance patients you most likely will not have to wait very long. I would say 2-4 weeks if you are already established with that doctor, and maybe 6-8 weeks if you are not. Again all of this depends on where you live.
Now if you are on public insurance your wait will probably be a lot longer because doctors who take public insurance usually take just about anyone and they are very busy. So if you are already established with them you will probably wait 6-8 weeks. Not established could be 3-4 months.
This all changes if you are needing a specialist. As the poster above me said they had to wait 11 months to see the doctor and they were already established. I think that is a bit ridiculous, but not out of the realm or possibility. Again, all of the above mentioned will have a factor as well on how quickly you see the specialist.
Now there is a huge trend here in the US with the over use of narcotics. There is a huge push to eliminate them as much as possible because of how many people are addicted to them no matter how they got that way. So, a lot of doctors tell you right up front, before you are even allowed to schedule, that if you are on narcotics for pain, or other narcotics for any reason, they will not let you establish there. If it's their policy to not accept pain patients then you will have to find another doctor. If you lie about being on narcotics, when the doctors office gets your chart and sees that you are in fact on chronic narcotics, you will be thrown out of the office, if you even make it that far. Also, if you think you are being sneaky and decide to tell the doctor that you didn't have a previous doctor so you won't have a chart from the old doctor. Well, there are ways around that too. Put your name into the I-Stop computer for example and it will pull you up and tell them exactly what medications you are on. And if you lied again, you will be kicked out and you will have to find another doctor which will add to your time.
For me what prompts me to get a physical every year is the fact that my insurance coverage goes down and the deductables go up if I don't get a physical every year, with supporting blood work for my medications. Also if I don't get a mammy done according to standard guidelines they can opt to greatly reduce my coverage for my treatments for anything related. So that's my incentive. LOL.
The main thing to remember here really is that all of this has variables which vary greatly depending on your insurance, where you live, whether or not you are established with that doctor or not, and what medications you are on. So really there isn't really one answer to any of your questions.