There's been a load of debate about the Prisoner running order over the years. When I was active in Prisoner fandom (nearly three decades ago now - blimey!) there used to be a lot of healthy discussion, lots of theories, and people emphasizing different aspects and preferences to arrive at their own preferred sequence. What I liked about it was that there was no definitive solution, and that the Six of One society never endorsed a final "approved" order, because of course, they respected the views of all their members, and the series is about the freedom of the individual after all. I haven't been a member of Six of One for years, mind you, but I understand they did eventually "endorse" a certain order which might be the one used on the US DVDs. Though as Six of One is almost completely irrelevant to Prisoner appreciation these days, and is pretty much a self-serving oligarchy, their endorsement shouldn't really count for much.
So my best advice is to watch the series, and make up your own mind. Decide how it works best for you and then stick to it. There is no real narrative structure or developement to the series.
For what it's worth, this is my preferred sequence, developed over many years of thought and debate. It derives partly from the production sequence, partly from the ITC order, and partly on three perceived narrative threads. Firstly, the increasing complexity and danger in the Village's attempts to break the Prisoner. Secondly, the shift in emphasis from episodes about the Prisoner discovering things about the village and trying to escape - to fighting the system from within and destroying the schemes of number 2. Thirdly (and developing out of the first two) the shift in the dynamics of power between the Prisoner and number 2.
Arrival
Free For All
Dance of the Dead
Checkmate
The Chimes of Big Ben
The Schizoid Man
It's Your Funeral
Many Happy Returns
Living in Harmony
The General
A. B. and C.
Do Not Forsake Me Oh My Darling
A Change of Mind
Hammer into Anvil
The Girl Who Was Death
Once upon a Time
Fall Out
But I don't expect there's anyone else who'll subscribe exactly to that ordering, which is as it should be.
I'm always a little bemused by this notion of the 7 "approved" McGoohan episodes. This seems to stem from some interview comments he made in the eighties that he wanted to do a 7 part mini-series, but Lew Grade wanted to commission a full season, so they were forced to come up with other ideas. It's hard to know how much truth there is in that or whether it was an invention years after the fact. I also recall McGoohan said, there were 7 episodes he'd keep and throw the rest away. But I've never been able to find a quote where he actually specified which 7 they were. The assumption in fandom seems to be that it's:
Arrival
Free For All
Dance of the Dead
Checkmate
The Chimes of Big Ben
Once upon a Time
Fall Out
which is the first six episodes in the production sequence (although Checkmate was filmed before Dance of the Dead) plus the conclusion. It occurs to me that fans decided that these must be the seven that McGoohan had in mind when he proposed his mini-series (if he did...) but it's hard to know that for sure. For one thing, how can we be sure Fall Out was in his mind when he started? Fall Out was hurriedly written over a weekend to wrap things up when Lew Grade pulled the plug on the production.
There's also the question that the completed footage for Dance of the Dead for instance sat on a shelf for months because no one thought that the episode was working, until finally the film editor suggested he could have a go at salvaging what was there into a completed episode.
Once upon a Time was shot sixth, but was that just because a script was ready at the time? It seems to have always been the intention to hold it back to conclude the first block of thirteen episodes, rather than just set up the concluding episode. The intention seems to have been to move the series out of the village in the second block of thirteen.
That sacred "McGoohan 7" list also means we lose complex and intelligent episodes like The General, Living in Harmony and A Change of Mind, which seem to me more key to the core themes of the series than say Checkmate or Chimes (though those are both enjoyable adventure stories).
So who knows? I don't.