Germany.
We have a public health system that works through public insurance, but also have a small private sector (wich a lot of rich people use and freelancers are forced to use, since employers usually pay over half of the cost of your health insurance). If you happen to be uninsured you still get treatments and the cost is delayed to the point in time when you have insurance again. Health insurance is mandatory. If you are unable to pay for it, the state will pay it for you.
I've never had to worry about medical cost throughout my life. Everything, from check-ups to long hospital visits is covered, as long as it is reasonably medically neccessary.
We have some small medication fees and have to pay full price for over the counter drugs, though. It's always manageable costs in the realm of up to 5€ or so.
Some of the changes that were made to the systems detriment (with the great forces of capitalism and the free market used as justification) are that for certain things you only get basic coverage and need either add-on insurances or have to pay out of your own pocket to pay it. Such things include a range of tooth related things, like nicer looking fillings, certain implants and tooth replacements, professional dental cleaning (unless you're wearing braces), etc.
It also includes all glasses unless you're over six dioptrin in any direction.
You can usually get a free frame and cheapo glasses for about 20€, but if you're going to be dependent on your glasses you will need them to be anti-reflective and anti scratch coated and maybe extra thin, depending on your frame and that will put you back 250€ - 350€ on average.
The most stupid thing about this is that they don't cover eye-laser surgery, because you could get glasses or contacs......wich they also don't cover....
All of this used to be covered at one point, but private insurances lobbied for them to be excluded from the public health insurances in order to make themselves and their elevated pricepoints look more attractive.
I''ve never had a problem to get to a GP, in fact you usually just go there and wait until it's your turn.
GPs aren't really bound to a certain district either, if you WANT to go across town every time you have a cold, because you prefer that GPs clinic, you're free to do so.
My particular GP doesn't do appointments, just open clinic, wich means first come, first serve. I was chummy with the team and used to call ahead to tell them to put me on the list and call me when it was nearly my turn if I was feeling too shit to sit in a waiting room for two hours, since I live next door, but now they changed a lot of the team and the new people wont do that anymore.
Getting an appointment with a specialist in a timely fashion can be a nightmare, I had to call 15 neurologists before I got to one that would even give me an appointment. My neurologist is great, but standart waiting times are 6-8 weeks, wich is very long if you have aomething that comes in acute flares and needs to be tested while it's there.
A huge problem with this is that they will flat out refuse to treat you, even though they are technically legally obligated to do so, if you're not either privately insured, or have a serious diagnosis like cancer treatment, both of wich will bring a lot more money in than other smaller, but also life-inhibiting problems.
There is a service number that will get you an appointment within three weeks in your area, but you cannot choose wich doctor you get, as one is appointed to you.
Overall, I'd say while there's problems with the system, it's nothing that is unsolvable. BS like preferencial treatment of privately insured people, or non payment for essencials like glasses need to be rolled back again and a lot of hospitals and clinics are in need of more good personnel.
The money for it is there though and it is a sustainable system, that overall keeps costs low, so I'd prefer it over whatever is happening in Brazil, the US or the Phillippines any day.