Cost-efficient? Then why are you looking at APP?! You can do your ATPL far more cheaply, as a casual look through this forum would show.
As for the likelihood of employment, the most important factor is the health of the airline industry at the time of your graduation. This is not something that's very easy to predict with any accuracy; there are several occasions over the last 10 years when considerably better-qualified observers than I have got it wrong!
When you go to Oxford (or any other school offering a similar course), have some fairly searching questions ready for their employment liaison people. Oxford claim a very high number of their students are employed by airlines within a short period of graduation. See if you can get specifics, and ask whether the rate has been consistent over, say, the last 10 years. It's easy to claim credit in the good years, but it's when times are more difficult that the true quality of the school's employment-seeking prcedures and personnel will become apparent.
Ask, also, what proportion of graduates found jobs through their own efforts, as opposed to those who were employed as a direct result of the school's efforts. Posts here over the last year or so suggest that some schools may not have been totally honest in their claims to have 'found employment' for their students - if, in fact, you are going to have to do all the leg work, what are you paying the school for?
Do not be too easily swayed by any school's marketing hype. They want to sell you their course so that they can make a profit out of you; they are not in this to get a warm and fuzzy feeling by being nice to people. They'll often tell you what they think you want to hear - so ask questions that make them reveal the downsides. For instance, how many fATPL graduates of their school do not get an airline job within a year of graduation? They won't want to tell you, because the number will be larger than they are comfortable with, but it's an essential point of comparison for you, and a reality check about what you are getting into.
There is no single guaranteed way of getting an airline job from scratch. The big schools would like you to believe that they have a monopoly on getting people into first jobs; they don't. For every APP graduate that gets hired, there are several modular students doing so. Don't get blinkered in your approach, look at all the options, and ask lots of searching questions especially when someone appears to start offering more than they can reasonably deliver!
Scroggs