So...the British monarchy acts under a system where sons inherit before daughters, and older children inherit before younger children. This seems highly unlikely to change anytime soon, but it does raise the question of, assuming you have to choose a monarch out of direct descendants based purely on age and gender, what particular algorithm is the ideal choice for the 21st century.
Before I move on, let me first say that this topic is not a discussion on whether or not England should still have a monarchy. (The answer is yes because it brings in truckloads of tourism money).
Let me also say that I firmly suspect that the question of who is next in line to Elizabeth II is probably completely irrelevant. She's 82, and in good health, and her mother lived past 100. By the time Lizzie is 110, presumably scientists will be able to transplant her brain into a robot (probably a little girl robot since we seem to be a lot better at building 3-foot biped robots than 6-foot biped robots), and then Lizzy-2 will reign as Robot Queen of England forever, and all will be right with the world.
So...anyhow, what are the qualities of the best monarchs in England, at least in terms of age and gender? A quick Google search points out the three candidates for greatest monarchs are...
http://news.bbc.co.uk/2/hi/uk_news/magazine/6936537.stmQueen VictoriaGender: female
Age: 18 when she took the throne
King Henry VIIIGender: male
Age: 17 when he took the throne
Queen ElizabethGender: female
Age: 24 when she took the throne
But...okay, what made a good monarch 500 years ago may not be what makes a good monarch today (notably, Henry VIII would be a bit of a disaster, what with the 8 wives and wanting to change the church of England). So...what makes a good monarch today? An interesting question. Looking at the duties that Elizabeth II performs (beyond just smile and wave), notably she meets and consults with the Prime Minister regularly. At first she was the student--famously the first Prime Minister she swore in (Sir Winston Churchill) said to her "girl, I'm going to teach you a thing or two about politics," 55 years of experience and consultation later she acts as a voice of wisdom and experience to the current Prime Minister, which actually sounds pretty useful to me. In other words, an ideal monarch would, much like Victoria, Elizabeth 1, and Henry 8, take the throne at a young age to experience a longer term.
Which raises the first concern about the current succession structure. In the unfortunate event that Super Robot Elizabeth does not happen, we'll see 80-year-old Charles succeed to the throne; not only would he have a relatively short time to build up the wisdom of the prime ministers, but 80-year-olds learn a lot slower than 18-year-olds so he'd absorb less of it during the same time. In fact, Elizabeth's youngest son would probably be at least 64 by the time she dies. Seems to me you should be prepared to look among grandchildren / great grandchildren as well. So the question becomes: how young do you go? Say, 2-year-old is obviously too young. Elizabeth II's father declined to take her on tour with him when she was 13, saying that she was too young for a strenuous month-long tour, and there's a fair bit of merit to that (for the same reason the olympics puts a minimum age on Gymnists--kids with unnatural stress when they're growing can get screwed up). Okay, but we have Victoria and Henry starting at 18 and 17 respectively; let's see...legal age to drive a car in England is 17; sure I guess--if you can drive a car you can rule a country. Okay, so how about the youngest direct descendant over the age of 17.
Next we come to gender. Now, arguably England's best monarchs have been queens (Henry VIII made a lot of changes, but that's not really what we're looking for in the modern day). Now, looking into why, among other things both Elizabeth and Victoria never married, keeping themselves open as bargaining chips; this is hardly relevant anymore. On the more relevant end, I've also heard the argument that the British were historically more willing to defend the honour of the queen, die for the queen, etc, which...is kinda relevant to the modern pure-figurehead role, actually. In practical considerations, going back to the age discussion, women stop growing earlier, and tend to live longer. In terms of symbolism, perhaps I'm cynical, but I suspect the elected prime minister will more often than not be male, so having a female symbol of power too is a nice balance. Statistically, teenage girls are less likely to commit murder than teenage boys, so the risk of "I just turned 17 and need the current monarch to die now" scenarios is somewhat lessened.
That said, while a lot of little things seem to be stacked towards females here, there is an argument for non-discrimination just because the monarch you get will be younger on-average if you don't discriminate. Which...well, let's run some statistics on the current royal family:
1952-1976 (0 years difference; same heir)
1977-1980 (10 years difference: Anne vs Andrew)
1981-1998 (14 years difference: Anne vs Edward)
1999-2000 (32 years difference: Anne vs William)
2001-2004 (34 years difference: Anne vs Harry)
2005-2023 (0 years difference; same heir)
2023-?? (4 years difference; Severn vs Louise)
Alternatively if the genders were reversed it would be mostly a 0-2 year gap until 2005 (4 year gap), then 2007 (6 year gap) then 2020 (19 year gap). Hmm...yeah, really not liking these 20-year-gaps; I guess fairness and equality win over sexism; sunshine and rainbows for everyone!
So...my proposal:
The youngest direct descendant over the age of 17.