Oh, crumbs. How to condense the British class system and the army that both typifies and breaks it into short paragraphs. Firstly, the rules are a little looser now than they were in the 60's, but the class system is still very much a part of our society. Please understand that these are massive, sweeping generalisations, and that I am not now nor have never been a soldier. I've spent a long time around the Forces looking in, but I don't have the experience to give you anything more than educated guesses.
The social classes are almost a caste system. The class of your parents determines your class, as the class of their parents determined theirs. It is possible for someone to change their class, but it's almost always a multi-generational effort, and starts with a family close to the 'borders' of their class - who had been of the other class a few generations back, or whose occupation straddles the borders.
The upper class are the nobility, the old money and the landowners (and proud of it). They are the ones who lead. 'Gentlemen' by definition, in the army they are also the 'officer' class and always have been. Most families who consider a particular regiment their family regiment are upper class, but becoming an officer was (and still remains) one of the classic roles for the upper class male. However, there aren't that many upper class males to start with, compared to the other classes.
The middle class are the intellectuals, the ones who think (and are proud of it). They can rise to the upper class over the generations, by sending their children to the right schools and having enough money, but they have a substantially different set of values. Most middle-class people remaining in the army in the 60's will have been officers, but some few will have been enlisted. They tend towards the younger regiments and the specialist trades, such as Military Intelligence, Communications and Engineering - the ones that require technical proficiency or other learning, more than those that require charismatic leadership. Compared to the upper and lower classes the middle class don't send many to the army, but there are a few families with military traditions and while a family regiment is not unheard of, a family occupation is more common.
The lower class are the working class, the ones who labour (and are proud of it). The vast majority of enlisted are lower class, while very few officers have a working class background. This is the other place where deep familial regimental ties are found, and this is where the 'area' a regiment is supposed to recruit from is most important. The regional regimental names are more than just places, they're where that regiment belongs and where most of its men belong to.
The socially elite regiments can have enlisted from almost anywhere, though there was often a set of criteria for getting in, based on wealth, possessions or background - a cavalryman in the pre-WWI days had to be able to ride, for instance.
The Paras are an elite regiment of another kind. They take only those enlisted men who have passed through a training regime designed to make sure that a Paratrooper is one of the best the army has to offer. I'm not sure about their officer criteria - that's not something I've ever looked at - but most Paras came from another regiment to start with (and some go on to SAS Selection, but that's another tale). Becoming a Para is an aspiration, rather than a default position, and as far as I understand it there are few conflicts between loyalty to the Paras and loyalty to the 'home' regiment.
Meanwhile, back to the question - a sergeant is typically a paragon of the working class, a solid and practical man with a wealth of experience who knows how to get things done. He's the go-to man when you don't know something, and it's his job to know everything. A married sergeant of that era would be expected to have a wife who's similar. Competent and capable, she would be expected to provide support and experience for the younger wives of the regiment, whatever their class. She'd be a veteran of moving herself and the children to another country with a few weeks' notice, of spending days and weeks without word from her husband, and of taking care of everything a husband was more usually expected to do in the pre-feminist era.
The officers' wives would in turn be expected to know how to work with older women of the working class. The class divide informs everything, but the gulf between upper and lower class is a lot wider than the gulf between middle and lower class. I suspect a larger proportion of wives in the Paras would have been middle class, rather than upper; the type of elitism involved lends itself more to those with aspirations than those who already know they are at the top of the heap.
There would be mutual respect between the wives, but in general the British know their place and aspire to better their family's lot, rather than wanting to bring the whole system crashing down. A sergeant is in one of those occupations which pushes the boundary between working class and middle class, for instance. The sergeant himself will remain working class, but his children or grandchildren may be able to make the transition, especially if his wife has made the right friends.
An American thrown into all this - none of which is written down anywhere - could make gaffe after gaffe after gaffe, all without realising it.
