Best Transition Career for Trading/ or FE Masters programs

So I was just reviewing my likely options upon graduation the other day, and it got me thinking about whether there may be careers that could allow me to transition from a non-target school to a BB/or Buy side trading position. (I realize that trading is a very specialized skill that is hard to pick up in any other field but I am talking about the smallest details here, like showing I deal well under pressure or understanding risk management)

I started thinking about applying to Masters in Finance/F.Eng/F.Math (Oxford/LSE, Chicago/Columbia/Berkley) programs as well but must first cram in some math/ programming classes my last year before I even send my app in. Thefefore I will likely have to work a year or two atleast before I can apply to one of these programs.

The likely scenario is that I will be trying to land some BO/MO job out of school since those are primarily the positions that recruit on the Northeastern campus. My question is:

Are there specific back or middle office jobs that would atleast add a slight advantage for getting into either trading or one of the masters programs listed above? (I was thinking along the lines of Trade support or Risk Management)

would there be other less convential jobs I should look at as well? (consulting/ non profit/ military/ research assistant for professor/ small prop shops/ day trade)

I was also thinking about perhaps a beginner job dealing with programming which could help me get into one of the financial engineering schools.